Recent zbMATH articles in MSC 54https://www.zbmath.org/atom/cc/542021-07-26T21:45:41.944397ZWerkzeugPrefacehttps://www.zbmath.org/1463.000092021-07-26T21:45:41.944397Z"Kumam, Poom"https://www.zbmath.org/authors/?q=ai:kumam.poom"Cho, Yeol Je"https://www.zbmath.org/authors/?q=ai:cho.yeol-je"Gopal, Dhananjay"https://www.zbmath.org/authors/?q=ai:gopal.dhananjaySpecial Issue of the 9th Asian Conference on Fixed Point Theory and Optimization (ACFPTO2016) on May 18--20, 2016 at Science Laboratory Building, Faculty of Science, King Mongkut's University of Technology Thonburi (KMUTT), Bangkok, Thailand.Tibor Neubrunn (1929--1990)https://www.zbmath.org/1463.010012021-07-26T21:45:41.944397Z"Dvurečenskij, Anatolij"https://www.zbmath.org/authors/?q=ai:dvurecenskij.anatolij"Holá, Ľubica"https://www.zbmath.org/authors/?q=ai:hola.lubica"Janková, Katarína"https://www.zbmath.org/authors/?q=ai:jankova.katarina"Riečan, Beloslav"https://www.zbmath.org/authors/?q=ai:riecan.beloslavThe book provides a picture of the personality of Tibor Neubrunn, one of the most significant Slovak mathematicians and mathematics pedagogues. The first part presents information on Neubrunn's life, including memories of members of his family, colleagues, friends, and students. The second part is devoted to his scientific work, especially to his contribution to measure theory, the theory of real functions and the theory of set valued functions. Neubrunn published four monographs and 56 scientific papers. Among other results, he provided the construction of a measure from a content and dealt with absolute continuity and dominancy of measures. In the field of real functions, he investigated various generalizations of the concept of continuity, above all quasicontinuity, and further closed graphs and multifunctions. Neubrunn initiated the study of quasicontinuous mappings and multifunctions in Slovakia and brought many doctoral students to this topic. Similarly, he initiated the Slovak research in the field of quantum logic, which received an international recognition. The monograph further discusses other results including set theory. The monograph is concluded with a full list of Neubrunn's publications and a supplement containing a photographic documentation.Colorful coverings of polytopes and piercing numbers of colorful \(d\)-intervalshttps://www.zbmath.org/1463.055332021-07-26T21:45:41.944397Z"Frick, Florian"https://www.zbmath.org/authors/?q=ai:frick.florian"Zerbib, Shira"https://www.zbmath.org/authors/?q=ai:zerbib.shiraSummary: We prove a common strengthening of Bárány's colorful Carathéodory theorem and the KKMS theorem. In fact, our main result is a colorful polytopal KKMS theorem, which extends a colorful KKMS theorem due to \textit{M.-H. Shih} and \textit{S.-N. Lee} [Math. Ann. 296, No. 1, 35--61 (1993; Zbl 0791.05007)] as well as a polytopal KKMS theorem due to \textit{H. Komiya} [Econ. Theory 4, No. 3, 463--466 (1994; Zbl 0858.54041)]. The (seemingly unrelated) colorful Carathéodory theorem is a special case as well. We apply our theorem to establish an upper bound on the piercing number of colorful \(d\)-interval hypergraphs, extending earlier results of \textit{G. Tardos} [Combinatorica 15, No. 1, 123--134 (1995; Zbl 0823.05022)] and \textit{T. Kaiser} [Discrete Comput. Geom. 18, No. 2, 195--203 (1997; Zbl 0883.05124)].Some remarks on the notations and terminology in the ordered set theoryhttps://www.zbmath.org/1463.060022021-07-26T21:45:41.944397Z"Păcurar, Mădălina"https://www.zbmath.org/authors/?q=ai:pacurar.madalina"Rus, Ioan A."https://www.zbmath.org/authors/?q=ai:rus.ioan-a(no abstract)Connectedness of intrinsic topologies of partial ordered setshttps://www.zbmath.org/1463.060082021-07-26T21:45:41.944397Z"Xu, Luoshan"https://www.zbmath.org/authors/?q=ai:xu.luoshan"Tang, Zhaoyong"https://www.zbmath.org/authors/?q=ai:tang.zhaoyongSummary: In this paper, the connectedness and local connectedness of partial ordered sets under various intrinsic topologies are further studied by considering the interactions of order and topology. The main results are as follows: (1) A partial ordered set is order-connected if and only if it is connected endowed with the Alexandrov topology if and only if it is connected endowed with the Scott topology. (2) Each partial ordered set endowed with the Alexandrov topology is locally connected, and every partial ordered set endowed with the Scott topology is also locally connected. (3) If the specialization order of a topological space is connected, then the topological space itself is connected. (4) A counterexample is constructed to show that a partial ordered set with the lower topology is connected, but the partial ordered set endowed with the Scott topology is not order-connected.When spectra of lattices of \(z\)-ideals are Stone-Čech compactifications.https://www.zbmath.org/1463.060422021-07-26T21:45:41.944397Z"Dube, Themba"https://www.zbmath.org/authors/?q=ai:dube.thembaSummary: Let \(X\) be a completely regular Hausdorff space and, as usual, let \(C(X)\) denote the ring of real-valued continuous functions on \(X\). The lattice of \(z\)-ideals of \(C(X)\) has been shown by \textit{J. Martínez} and \textit{E. R. Zenk} [Commentat. Math. Univ. Carol. 46, No. 4, 607--636 (2005; Zbl 1121.06009)] to be a frame. We show that the spectrum of this lattice is (homeomorphic to) \(\beta X\) precisely when \(X\) is a \(P\)-space. This we actually show to be true not only in spaces, but in locales as well. Recall that an ideal of a commutative ring is called a \(d\)-ideal if whenever two elements have the same annihilator and one of the elements belongs to the ideal, then so does the other. We characterize when the spectrum of the lattice of \(d\)-ideals of \(C(X)\) is the Stone-Čech compactification of the largest dense sublocale of the locale determined by \(X\). It is precisely when the closure of every open set of \(X\) is the closure of some cozero-set of \(X\).On minimal ideals in the ring of real-valued continuous functions on a frame.https://www.zbmath.org/1463.060432021-07-26T21:45:41.944397Z"Karimi Feizabadi, Abolghasem"https://www.zbmath.org/authors/?q=ai:karimi-feizabadi.abolghasem"Estaji, Ali Akbar"https://www.zbmath.org/authors/?q=ai:estaji.ali-akbar"Abedi, Mostafa"https://www.zbmath.org/authors/?q=ai:abedi.mostafaSummary: Let \(\mathcal{R}L\) be the ring of real-valued continuous functions on a frame \(L\). The aim of this paper is to study the relation between minimality of ideals \(I\) of \(\mathcal{R}L\) and the set of all zero sets in \(L\) determined by elements of \(I\). To do this, the concepts of coz-disjointness, coz-spatiality and coz-density are introduced. In the case of a coz-dense frame \(L\), it is proved that the \(f\)-ring \(\mathcal{R}L\) is isomorphic to the \(f\)-ring \(C(\Sigma L)\) of all real continuous functions on the topological space \(\Sigma L\). Finally, a one-one correspondence is presented between the set of isolated points of \(\Sigma L\) and the set of atoms of \(L\).Quasi-semi-homomorphisms and generalized proximity relations between Boolean algebrashttps://www.zbmath.org/1463.060792021-07-26T21:45:41.944397Z"Celani, Sergio A."https://www.zbmath.org/authors/?q=ai:celani.sergio-arturoSummary: In this paper we shall define the notion of quasi-semi-homomorphisms between Boolean algebras, as a generalization of the quasi-modal operators introduced in \textit{S. Celani} [Math. Bohem. 126, No. 4, 721--736 (2001; Zbl 0999.06012)], of the notion of meet-homomorphism, and the notion of precontact or proximity relation. We will prove that the class of Boolean algebras with quasi-semi-homomorphism is a category, denoted by \textbf{BoQS}. We shall prove that this category is equivalent to the category \textbf{StQB} of Stone spaces where the morphisms are binary relations, called quasi-Boolean relations, satisfying additional conditions. This duality extends the duality for meet-homomorphism and the duality for quasi-modal operators.Free ideals and real ideals of the ring of frame maps from \(\mathcal{P}(\mathbb{R})\) to a framehttps://www.zbmath.org/1463.060882021-07-26T21:45:41.944397Z"Estaji, Ali Akbar"https://www.zbmath.org/authors/?q=ai:estaji.ali-akbar"Mahmoudi Darghadam, Ahmad"https://www.zbmath.org/authors/?q=ai:mahmoudi-darghadam.ahmadSummary: Let \(\mathcal{F_P}(L)\text{ }(\mathcal{F^{\ast}_P}(L))\) be the \(f\)-rings of all (bounded) frame maps from \(\mathcal{P}(\mathbb{R})\) to a frame \(L\). \(\mathcal{F_{P_{\infty}}}(L)\) is the family of all \(f\in\mathcal{F_P}(L)\) such that \(\uparrow f(-\frac{1}{n},\frac{1}{n})\) is compact for any \(n\in\mathbb{N}\) and the subring \(\mathcal{F_{P_K}}(L)\) is the family of all \(f\in\mathcal{F_P}(L)\) such that \(\text{coz}(f)\) is compact. We introduce and study the concept of real ideals in \(\mathcal{F_P}(L)\) and \(\mathcal{F^{\ast}_P}(L)\). We show that every maximal ideal of \(\mathcal{F^{\ast}_P}(L)\) is real, and also we study the relation between the conditions ``\(L\) is compact'' and ``every maximal ideal of \(\mathcal{F_P}(L)\) is real''. We prove that for every nonzero real Riesz map \(\varphi:\mathcal{F_P}(L)\rightarrow\mathbb{R}\), there is an element \(p\) in \(\Sigma L\) such that \(\varphi=\tilde{p_{\text{coz}}}\) if \(L\) is a zero-dimensional frame for which \(B(L)\) is a sub-\(\sigma\)-frame of \(L\) and every maximal ideal of \(\mathcal{F_P}(L)\) is real. We show that \(\mathcal{F_{P_{\infty}}}(L)\) is equal to the intersection of all free maximal ideals of \(\mathcal{F^{\ast}}_P(L)\) if \(B(L)\) is a sub-\(\sigma\)-frame of a zero-dimensional frame \(L\) and also, \(\mathcal{F_{P_K}}(L)\) is equal to the intersection of all free ideals \(\mathcal{F_P}(L)\) (resp., \(\mathcal{F^{\ast}_P}(L))\) if \(L\) is a zero-dimensional frame. Also, we study free ideals and fixed ideals of \(\mathcal{F_{P_{\infty}}}(L)\) and \(\mathcal{F_{P_K}}(L)\).Algebraic and topological aspects of quasi-prime idealshttps://www.zbmath.org/1463.130132021-07-26T21:45:41.944397Z"Aghajani, M."https://www.zbmath.org/authors/?q=ai:aghajani.mohsen"Tarizadeh, A."https://www.zbmath.org/authors/?q=ai:tarizadeh.abolfazlSummary: In this paper, we define the new notion of quasi-prime ideal which generalizes at once both prime ideal and primary ideal notions. Then a natural topology on the set of quasi-prime ideals of a ring is introduced which admits the Zariski topology as a subspace topology. The basic properties of the quasi-prime spectrum are studied and several interesting results are obtained. Specially, it is proved that if the Grothendieck t-functor is applied on the quasi-prime spectrum then the prime spectrum is deduced. It is also shown that there are the cases that the prime spectrum and quasi-prime spectrum do not behave similarly. In particular, natural topological spaces without closed points are obtained.The applications of the universal morphisms of \underbar{CF-TOP} the category of all fuzzy topological spaceshttps://www.zbmath.org/1463.180112021-07-26T21:45:41.944397Z"Ismail, Farhan"https://www.zbmath.org/authors/?q=ai:ismail.farhan"Latreche, Abdelkrim"https://www.zbmath.org/authors/?q=ai:latreche.abdelkrimSummary: In the present work, we built a category of fuzzy topological spaces from Chang's definition of Fuzzy TOPological space, that we denoted \underbar{CF-TOP}. Firstly, we collected universal morphisms of \underbar{TOP} category, listed by \textit{S. Mac Lane} [Graduate Texts in Mathematics. 5. New York-Heidelberg-Berlin: Springer-Verlag. IX, 262 p. (1971; Zbl 0232.18001)], then, we studied universal morphisms of \underbar{CF-TOP}. This study shows that these morphisms are just generalizations of \underbar{TOP} category morphisms, which confirms that Chang's fuzziness to topological space is weak. At the end of this work, we prove that \underbar{TOP} and \underbar{CF-TOP} are not isomorphic.On ideal topological groupshttps://www.zbmath.org/1463.220012021-07-26T21:45:41.944397Z"Jafari, S."https://www.zbmath.org/authors/?q=ai:jafari.saeid.2|jafari.sepehr|jafari.sajad|jafari.s-akbar|jafari.shahnaz|jafari.shahla|jafari.shahram|jafari.saeid|jafari.samira|jafari.saeid.1|jafari.sayyed-heidar|jafari.somaye|jafari.somayeh|jafari.saeed|jafari.s-a-m"Rajesh, N."https://www.zbmath.org/authors/?q=ai:rajesh.n-r|rajesh.neelamegarajan|rajesh.namegaleshLet \((G, \ast,\tau, \mathcal{I})\) be a group \((G,\ast)\) equipped with a topology \(\tau\) and an ideal \(\mathcal{I}\) on \(G\). A subset \(S\) of \(G\) is called \(\mathcal{I}\)-open if \(S \subset\) Int\((S^*)\), where \(S^* = \{x \in G: U\cap S \notin \mathcal{I}\) for every neighbourhood \(U\) of \(x\}\). A mapping \(f\) between ideal spaces \((X,\tau,\mathcal{I})\) and \((Y, \sigma,\mathcal{I})\) is said \(\mathcal{I}\)-continuous if the preimage \(f^{-1}(V)\) of any open set \(V \subset Y\) is \(\mathcal{I}\)-open in \(X\). The authors study ideal topological groups by using \(\mathcal{I}\)-open sets and \(\mathcal{I}\)-continuity: an ideal topologized group \((G, \ast,\tau, \mathcal{I})\) is an ideal topological group if the group operations \((x,y) \mapsto x\ast y\) and \(x\mapsto x^{-1}\) are \(\mathcal{I}\)-continuous. Several basic properties of these groups, similar to properties of classical topological groups, are established.Fixed point of continuous mappings defined on an arbitrary intervalhttps://www.zbmath.org/1463.260032021-07-26T21:45:41.944397Z"Alagoz, Osman"https://www.zbmath.org/authors/?q=ai:alagoz.osman"Gunduz, Birol"https://www.zbmath.org/authors/?q=ai:gunduz.birol"Akbulut, Sezgin"https://www.zbmath.org/authors/?q=ai:akbulut.sezginSummary: In this work, we consider an iterative method given by \textit{N. Karaca} and \textit{I. Yildirim} [J. Adv. Math. Stud. 8, No. 2, 257--264 (2015; Zbl 1343.47069)] to approximate fixed point of continuous mappings defined on an arbitrary interval. Then, we give a necessary and sufficient condition for convergence theorem. We also compare the rate of convergence between the other iteration methods. Finally, we provide a numerical example which supports our theoretical results. Our findings improve corresponding results in the contemporary literature.Wijsman quasi-invariant convergencehttps://www.zbmath.org/1463.400062021-07-26T21:45:41.944397Z"Gülle, Esra"https://www.zbmath.org/authors/?q=ai:gulle.esra"Ulusu, Uǧur"https://www.zbmath.org/authors/?q=ai:ulusu.ugurSummary: In this study, we defined concepts of Wijsman quasi-invariant convergence, Wijsman quasi-strongly invariant convergence and Wijsman quasi-strongly \(q\)-invariant convergence. Also, we give the concept of Wijsman quasi-invariant statistically convergence. Then, we study relationships among these concepts. Furthermore, we investigate relationship between these concepts and some convergence types given earlier for sequences of sets, too.Lacunary invariant statistical convergence of double sequences of setshttps://www.zbmath.org/1463.400092021-07-26T21:45:41.944397Z"Nuray, Fatih"https://www.zbmath.org/authors/?q=ai:nuray.fatih"Ulusu, Uǧur"https://www.zbmath.org/authors/?q=ai:ulusu.ugurSummary: In this paper, we introduce the concepts of Wijsman invariant convergence, Wijsman invariant statistical convergence, Wijsman lacunary invariant convergence, Wijsman lacunary invariant statistical convergence for double sequences of sets. Also, we investigate existence of some relations among these new convergence concepts for double sequences of sets.On almost asymptotically lacunary statistical equivalence of sequences of setshttps://www.zbmath.org/1463.400142021-07-26T21:45:41.944397Z"Ulusu, Uğur"https://www.zbmath.org/authors/?q=ai:ulusu.ugurSummary: In this paper we study the concepts of Wijsman almost asymptotically statistical equivalent, Wijsman almost asymptotically lacunary statistical equivalent and Wijsman strongly almost asymptotically lacunary equivalent sequences of sets and investigate the relationship between them.Some topological properties of the set of filter cluster functionshttps://www.zbmath.org/1463.400192021-07-26T21:45:41.944397Z"Albayrak, Hüseyin"https://www.zbmath.org/authors/?q=ai:albayrak.huseyin"Pehlivan, Serpil"https://www.zbmath.org/authors/?q=ai:pehlivan.serpil"Mohapatra, Ram N."https://www.zbmath.org/authors/?q=ai:mohapatra.ram-narayanSummary: In [the first and second author, Filomat 27, No. 8, 1373--1383 (2013; Zbl 1324.40007)], we generalized the concepts of pointwise convergence, uniform convergence and \(\alpha\)-convergence for sequences of functions on metric spaces by using the filters on $\mathbb N$. In this work, we define the concepts of limit function, \(\mathcal{F}\)-limit function and \(\mathcal{F}\)-cluster function respectively for each of these three types of convergence, where \(\mathcal{F}\) is a filter on $\mathbb N$. We investigate some topological properties of the sets of \(\mathcal{F}\)-pointwise cluster functions, \(\mathcal{F}\)-\(\alpha\)-cluster functions and \(\mathcal{F}\)-uniform cluster functions by using pointwise and uniform convergence topologies.An extension about Wijsman \(\mathcal I\)-asymptotically \(\lambda\)-statistical equivalencehttps://www.zbmath.org/1463.400242021-07-26T21:45:41.944397Z"Gumus, Hafize"https://www.zbmath.org/authors/?q=ai:gumus.hafize-gokSummary: In this study we extend the notions Wijsman \(\mathcal I\)-asymptotically \(\lambda\)-statistical equivalent sequences, Wijsman strongly \(\mathcal I\)-asymptotically \(\lambda\)-equivalent sequences and Wijsman strongly Cesáro \(\mathcal I\)-asymptotically equivalent sequences by using the sequence \(p=(p_k)\) which is the sequence of positive real numbers and \(\lambda=(\lambda_n)\) is a non-decreasing sequence of positive numbers tending to \(\infty\) such that \(\lambda_{n+1}\leq\lambda_n+1\) and \(\lambda_1=1\).On Wijsman asymptotically lacunary \(\mathcal{I}\)-statistical equivalence of weight $g$ of sequence of setshttps://www.zbmath.org/1463.400252021-07-26T21:45:41.944397Z"Kişi, Omer"https://www.zbmath.org/authors/?q=ai:kisi.omerSummary: This paper presents the following definition which is a natural combination of the definitions of asymptotically equivalence, \(\mathcal{I}\)-convergence, statistical limit, lacunary sequence, and Wijsman convergence of weight \(g\); where \(g:\mathbb{N}\to[0,\infty)\) is a function satisfying \(\lim_{n\to\infty}g(n)=\infty\) and \(\frac{n}{g(n)}\nrightarrow 0\) as \(n\to\infty\) for sequence of sets. Let \((X,\rho)\) be a metric space, \(\theta=\{k_r\}\) be a lacunary sequence and \(\mathcal{I}\subseteq 2^\mathbb{N}\) be an admissible ideal. For any non-empty closed subsets \(A_k,B_k\subseteq X\) such that \(d(x,A_k)>0\) and \(d(x,B_k)>0\) for each \(x\in X\), we say that the sequences \(\{A_k\}\) and \(\{B_k\}\) are Wijsman \(\mathcal{I}\)-asymptotically lacunary statistical equivalent of multiple \(L\) of weight \(g\) if for every \(\varepsilon>0,\delta>0\) and for each \(x\in X\), \[ \left\{r\in\mathbb{N}:\frac{1}{g(h_r)}\left\vert\left\{k\in I_r:\left\vert \frac{d(x,A_k)}{d(x,B_k)}-L\right\vert\ge\varepsilon\right\}\right\vert\ge \delta\right\}\in\mathcal{I} \] (denoted by \(A_k\overset{S^L_\theta(\mathcal{I}_W)^g}\to\sim B_k)\). We mainly investigate their relationship and also make some observations about these classes.The complete completeness of open mapping and spacehttps://www.zbmath.org/1463.460042021-07-26T21:45:41.944397Z"Bian, Hong"https://www.zbmath.org/authors/?q=ai:bian.hong"Qiu, Chongyi"https://www.zbmath.org/authors/?q=ai:qiu.chongyi"Yu, Haizheng"https://www.zbmath.org/authors/?q=ai:yu.haizhengSummary: In this paper, we aim to present a new proof for the theorem: if the continuous and almost open linear mapping from the local convex space \(E\) to arbitrary local convex space is always open mapping, then \(E\) is complete. Under the condition of separated locally convex space, making use of the properties that the range of conjugate mappings of continuous open linear mappings is weakly closed, we prove that if \(E\) is separated locally convex space, and the continuous and almost open linear mapping from the local convex space \(E\) to arbitrary local convex space is always open mapping, then \(E\) is complete.Invertibility of multivalued sublinear operatorshttps://www.zbmath.org/1463.471492021-07-26T21:45:41.944397Z"Orlov, Igor Vladimirovich"https://www.zbmath.org/authors/?q=ai:orlov.igor-v"Smirnova, Svetlana Ivanovna"https://www.zbmath.org/authors/?q=ai:smirnova.svetlana-ivanovnaSummary: We consider the representation of a compact-valued sublinear operator \((K\)-operator) by means of the compact convex packet of single-valued so-called basis selectors. Such representation makes it possible to introduce the concept of an invertible \(K\)-operator via invertible selectors. The extremal points of direct and inverse selector representations are described, an analogue of the von Neumann theorem is obtained. A series of examples is considered.Some new results of M-iteration process in hyperbolic spaceshttps://www.zbmath.org/1463.471572021-07-26T21:45:41.944397Z"Şahin, Aynur"https://www.zbmath.org/authors/?q=ai:sahin.aynurSummary: In this paper, we study the M-iteration process in hyperbolic spaces and prove some strong and \(\triangle\)-convergence theorems of this iteration process for generalized nonexpansive mappings. Moreover, we establish the weak \(w^2\)-stability and data dependence theorems for a class of contractive-type mappings by using M-iteration process. The results presented here extend and improve some recent results announced in the current literature.Fixed point theorems for generalized non-expansive mappingshttps://www.zbmath.org/1463.471592021-07-26T21:45:41.944397Z"Chandra, N."https://www.zbmath.org/authors/?q=ai:chandra.naveen"Joshi, Mahesh C."https://www.zbmath.org/authors/?q=ai:joshi.mahesh-chandra"Singh, Narendra K."https://www.zbmath.org/authors/?q=ai:singh.narendra-kumarSummary: In this paper, we obtain a fixed point theorem for the mappings satisfying non-expansive type conditions.Fixed point theorems for nonself Bianchini type contractions in Banach spaces endowed with a graphhttps://www.zbmath.org/1463.471602021-07-26T21:45:41.944397Z"Horvat-Marc, Andrei"https://www.zbmath.org/authors/?q=ai:horvat-marc.andrei"Balog, Laszlo"https://www.zbmath.org/authors/?q=ai:balog.laszloSummary: In this paper we present an extension of fixed point theorem for self mappings on metric spaces endowed with a graph and which satisfies a Bianchini contraction condition. We establish conditions which ensure the existence of fixed point for a non-self Bianchini contractions \(T:K\subset X\to X\) that satisfy Rothe's boundary condition \(T(\partial K)\subset K\).Best proximity point theorems for weak cyclic Bianchini contractionshttps://www.zbmath.org/1463.471622021-07-26T21:45:41.944397Z"Petric, Mihaela Ancuţa"https://www.zbmath.org/authors/?q=ai:petric.mihaela-ancutaSummary: Following the technique introduced in \textit{A. A. Eldred} and \textit{P. Veeramani} [J. Math. Anal. Appl. 323, No. 2, 1001--1006 (2006; Zbl 1105.54021)], in this paper we will extend Bianchini's fixed point theorem to a best proximity point type theorem. We introduce a new class of contractive conditions, called weak cyclic Bianchini contractions.Generalized fixed point theorems of Pandhare and Waghmode in Hilbert spacehttps://www.zbmath.org/1463.471642021-07-26T21:45:41.944397Z"Seshagiri Rao, N."https://www.zbmath.org/authors/?q=ai:seshagiri-rao.n"Kalyani, K."https://www.zbmath.org/authors/?q=ai:kalyani.karusalaSummary: This paper elucidates the existence and uniqueness of a fixed point to a self mapping over a closed subset of Hilbert space with rational expressions in the contraction inequality. This result is developed for a pair of mappings, positive integers powers of a pair of mappings, and again further extended to a sequence of mappings in the space. Moreover, special cases assure that these results are generalizations of well-known proven important results. Our results mainly focus on the generalization of the Pandhare and Waghmode result in Hilbert space [\textit{D. M. Pandhare} and \textit{B. B. Waghmode}, Math. Educ. 28, No. 4, 189--193 (1994; Zbl 0910.47053)].Existence results for systems of quasi-variational relationshttps://www.zbmath.org/1463.471732021-07-26T21:45:41.944397Z"Inoan, Daniela Ioana"https://www.zbmath.org/authors/?q=ai:inoan.daniela-ioanaSummary: The existence of solutions for a system of variational relations, in a general form, is studied using a fixed point result for contractions in metric spaces. As a particular case, sufficient conditions for the existence of solutions of a system of quasi-equilibrium problems are given.Some convergence and data dependence results for various fixed point iterative methodshttps://www.zbmath.org/1463.472092021-07-26T21:45:41.944397Z"Karakaya, Vatan"https://www.zbmath.org/authors/?q=ai:karakaya.vatan"Gürsoy, Faik"https://www.zbmath.org/authors/?q=ai:gursoy.faik"Ertürk, Müzeyyen"https://www.zbmath.org/authors/?q=ai:erturk.muzeyyenSummary: We have compared rate of convergence among various iterative methods. Also, we have established an equivalency result between convergence of two recently introduced iterative methods and we prove a data dependence result for one of them.Comments on convergence rates of Mann and Ishikawa iterative schemes for generalized contractive operatorshttps://www.zbmath.org/1463.472102021-07-26T21:45:41.944397Z"Kumar, Vivek"https://www.zbmath.org/authors/?q=ai:kumar.vivekSummary: In [Stud. Univ. Babeş-Bolyai, Math. 54, No. 4, 103--114 (2009; Zbl 1222.47106)], \textit{J. O. Olaleru} made the claim that Mann iteration converges faster than Ishikawa iteration when applied to generalized contractive operators. By providing an example we prove that this claim is false.Strong and \(\Delta\)-convergence of modified two-step iterations for nearly asymptotically nonexpansive mappings in hyperbolic spaceshttps://www.zbmath.org/1463.472152021-07-26T21:45:41.944397Z"Saluja, G. S."https://www.zbmath.org/authors/?q=ai:saluja.gurucharan-singhSummary: The aim of this article is to establish a \(\Delta\)-convergence and some strong convergence theorems of modified two-step iterations for two nearly asymptotically nonexpansive mappings in the setting of hyperbolic spaces. Our results extend and generalize the previous work from the current existing literature.Soft continuity and SP-continuityhttps://www.zbmath.org/1463.540012021-07-26T21:45:41.944397Z"Arar, Murad M."https://www.zbmath.org/authors/?q=ai:arar.murad-mSummary: Soft points are first introduced in 2012, and in the same year the soft mapping \(f_{pu}:SS(V)_A\to SS(V)_B\) and \textit{pu-continuity} are introduced. In this paper we re-define a soft set \((F, A)\) by its set of soft points \((\ddot{F},\ddot{A})\) (will be called \(sp\)-set); and study \(sp\)-sets properties. Then we define \textit{sp-function} and \textit{sp-continuity} and study their properties. The main result is that any soft mapping \(f_{pu}\) is \textit{pu-continuous} if and only if its corresponding \textit{sp-function} \(\ddot{f_{pu}}\) is \textit{sp-continuous}.New generalized closed sets in ideal nanotopological spaceshttps://www.zbmath.org/1463.540022021-07-26T21:45:41.944397Z"Asokan, Raghavan"https://www.zbmath.org/authors/?q=ai:asokan.raghavan"Nethaji, Ochanan"https://www.zbmath.org/authors/?q=ai:nethaji.ochanan"Rajasekaran, Ilangovan"https://www.zbmath.org/authors/?q=ai:rajasekaran.ilangovanSummary: We have introduce \(\mathcal{L}\)-\(nI_g\)-closed subsets, \(\mathcal{S}\)-\(nI_g\)-closed subsets, \(\mathcal{R}\)-\(nI_g\)-closed subsets and \(nI^*\)-\(\mathcal{O}\)-sets in this paper. Also we have discussed their properties related to other subsets.Diagnoses of medical image using nano digital topologyhttps://www.zbmath.org/1463.540032021-07-26T21:45:41.944397Z"Bhuvaneswari, K."https://www.zbmath.org/authors/?q=ai:bhuvaneswari.kasi"Priyadharshini, J. Sheeba"https://www.zbmath.org/authors/?q=ai:priyadharshini.j-sheebaSummary: In this paper the new concept of nano topological boundary approach is introduced to identify the bone fracture in it digital images.On decomposition of bioperation-continuityhttps://www.zbmath.org/1463.540042021-07-26T21:45:41.944397Z"Carpintero, Carlos"https://www.zbmath.org/authors/?q=ai:carpintero.carlos-r"Rajesh, Namegalesh"https://www.zbmath.org/authors/?q=ai:rajesh.namegalesh"Rosas, Ennis"https://www.zbmath.org/authors/?q=ai:rosas.ennis-rThis paper deals with some new type of sets defined by bioperation. By using them a new decomposition of bioperation-continuity is obtained. More precisely, 12 Definitions are proposed (some of them given by the authors) as well as 9 Propositions and Theorems, equipped with short and simple proofs.Mininal \(S_{\beta}\)-open sets and maximal \(S_{\beta}\)-closed sets in topological spaceshttps://www.zbmath.org/1463.540052021-07-26T21:45:41.944397Z"Jongrak, Ardoon"https://www.zbmath.org/authors/?q=ai:jongrak.ardoonSummary: In this work, new classes of sets called minimal \(S_{\beta}\)-open set and maximal \(S_{\beta}\)-closed set in topological spaces which were subclasses of \(S_{\beta}\)-open and \(S_{\beta}\)-closed sets respectively are introduced. We proved that the complement of minimal \(S_{\beta}\)-open set was maximal \(S_{\beta}\)-closed set. Some properties of the new concept of both sets were studied.Mildly \(\alpha\) generalized closed sets and its closed mappingshttps://www.zbmath.org/1463.540062021-07-26T21:45:41.944397Z"Kokilavani, V."https://www.zbmath.org/authors/?q=ai:kokilavani.v"Priyadarshini, S. Meena"https://www.zbmath.org/authors/?q=ai:priyadarshini.s-meenaSummary: In this paper, we define new types of closed sets called mildly \(\alpha\) generalized closed sets and mildly \(\alpha\) generalized closed mappings and study some of their properties. The relations with other notions directly or indirectly connected with mildly \(\alpha\) generalized closed sets are investigated.The pseudo \(e\)-topology and the pseudo \(\rho\)-topology on abstract baseshttps://www.zbmath.org/1463.540072021-07-26T21:45:41.944397Z"Mao, Xuxin"https://www.zbmath.org/authors/?q=ai:mao.xuxin"Xu, Luoshan"https://www.zbmath.org/authors/?q=ai:xu.luoshanSummary: The new concepts of the pseudo \(e\)-topology and the pseudo \(\rho\)-topology on abstract bases are introduced. Some basic properties of the pseudo \(e\)-topology and the pseudo \(\rho\)-topology and relations with other intrinsic topologies are explored. Via the pseudo \(e\)-topology and the pseudo \(\rho\)-topology, we obtain several characterizations of auxiliary bases of posets with auxiliary relations. It is proved that, in posets with auxiliary relations, auxiliary bases correspond exactly to dense sets with respect to the pseudo \(\rho\)-topology.New generalized classes of an ideal nanotopological spacehttps://www.zbmath.org/1463.540082021-07-26T21:45:41.944397Z"Nethaji, Ochanan"https://www.zbmath.org/authors/?q=ai:nethaji.ochanan"Asokan, Raghavan"https://www.zbmath.org/authors/?q=ai:asokan.raghavan"Rajasekaran, Ilangovan"https://www.zbmath.org/authors/?q=ai:rajasekaran.ilangovanSummary: In this paper, we introduce a new class of subsets called \(\xi\)-\(nI\)-open subsets and \(\mathcal{Q}\)-\(nI\)-closed subsets, where \(\xi\)-\(nI\)-open subsets are weaker than \(\alpha\)-\(nI\)-open subsets and \(\mathcal{Q}\)-\(nI\)-closed subsets are stronger than \(\beta\)-\(nI\)-open subsets. Also a new class of subsets called semi*-\(nI\)-closed subsets is introduced which are equivalent to \(t\)-\(nI\)-sets.Locally small spaces with an applicationhttps://www.zbmath.org/1463.540092021-07-26T21:45:41.944397Z"Piȩkosz, A."https://www.zbmath.org/authors/?q=ai:piekosz.arturSummary: We develop the theory of locally small spaces in a new simple language and apply this simplification to re-build the theory of locally definable spaces over structures with topologies.On rough bi-semi generalized continuous maps in rough set bitopological spaceshttps://www.zbmath.org/1463.540102021-07-26T21:45:41.944397Z"Priyadharshini, J. Sheeba"https://www.zbmath.org/authors/?q=ai:priyadharshini.j-sheeba"Bhuvaneswari, K."https://www.zbmath.org/authors/?q=ai:bhuvaneswari.kasiSummary: The purpose of this paper is to introduce and study the concepts of new class of maps, namely rough bi-semi generalized continuous maps in rough bitopological spaces. Also derive their characterizations in terms of rough bi-semi generalized closed sets, rough bi-semi-generalized closure and rough bi-semi generalized interior and obtain some of their properties.A new form of some nano setshttps://www.zbmath.org/1463.540112021-07-26T21:45:41.944397Z"Rajasekaran, Ilangovan"https://www.zbmath.org/authors/?q=ai:rajasekaran.ilangovan"Nethaji, Ochanan"https://www.zbmath.org/authors/?q=ai:nethaji.ochananSummary: In this paper, we made an attempt to notions of nano \(t^\#\)-set, nano \(\mathcal{B}^\#\)-set, nano \(t_\alpha\)-set, nano \(\mathcal{B}_\alpha\)-set and strong nano \(\mathcal{B}\)-set are introduced and investigated.Almost-s-Hurewicz ditopological texture spaceshttps://www.zbmath.org/1463.540122021-07-26T21:45:41.944397Z"Ullah, Hafiz"https://www.zbmath.org/authors/?q=ai:ullah.hafiz"Khan, Moiz ud Din"https://www.zbmath.org/authors/?q=ai:khan.moiz-ud-dinSummary: In this study the notion of almost-s-Hurewicz property in ditopological texture spaces is introduced thoroughly. We study the interrelation between Hurewicz, s-Hurewicz and almost-s-Hurewicz spaces. Also we give some characterizations in terms of regular open sets and various continuous mappings. Some properties of almost-s-compactness and almost-s- stability in setting of ditopological texture spaces are discussed.Lower power structures of directed spaceshttps://www.zbmath.org/1463.540132021-07-26T21:45:41.944397Z"Xie, Xiaolin"https://www.zbmath.org/authors/?q=ai:xie.xiaolin"Kou, Hui"https://www.zbmath.org/authors/?q=ai:kou.huiSummary: Powerdomains in domain theory play an important role in modeling the semantics of nondeterministic functional programming languages. In this paper, we extend the notion of powerdomain to the category of directed spaces and define the notion of lower powerspace of a directed space in the way of free algebras. Then we prove the existence of the lower powerspace over any directed space and give its concrete structure. Generally, the lower powerspace of a directed space is different from the lower powerdomain of a dcpo endowed with the Scott topology and the observationally-induced lower powerspace.On Hattori spaces.https://www.zbmath.org/1463.540142021-07-26T21:45:41.944397Z"Bouziad, A."https://www.zbmath.org/authors/?q=ai:bouziad.ahmed"Sukhacheva, E."https://www.zbmath.org/authors/?q=ai:sukhacheva.e-sSummary: For a subset \(A\) of the real line \(\mathbb{R}\), Hattori space \(H(A)\) is a topological space whose underlying point set is the reals \(\mathbb{R}\) and whose topology is defined as follows: points from \(A\) are given the usual Euclidean neighborhoods while remaining points are given the neighborhoods of the Sorgenfrey line. In this paper, among other things, we give conditions on \(A\) which are sufficient and necessary for \(H(A)\) to be respectively almost Čech-complete, Čech-complete, quasicomplete, Čech-analytic and weakly separated (in Tkachenko's sense). Some of these results solve questions raised by \textit{V. A. Chatyrko} and \textit{Y. Hattori} [Commentat. Math. Univ. Carol. 54, No. 2, 189--196 (2013; Zbl 1289.54020)].New approaches of inverse soft rough sets and their applications in a decision making problemhttps://www.zbmath.org/1463.540152021-07-26T21:45:41.944397Z"Demirtas, Naime"https://www.zbmath.org/authors/?q=ai:demirtas.naime"Hussain, Sabir"https://www.zbmath.org/authors/?q=ai:hussain.sabir"Dalkilic, Orhan"https://www.zbmath.org/authors/?q=ai:dalkilic.orhanSummary: We present inverse soft rough sets by using inverse soft sets and soft rough sets. We study different approaches for inverse soft rough set and examine the relationships between them. We also discuss and explore the basic properties for these approaches. Moreover we develop an algorithm following these concepts and apply it to a decision-making problem to demonstrate the applicability of the proposed methods.Statistical convergence of sequences of functions with values in semi-uniform spaces.https://www.zbmath.org/1463.540162021-07-26T21:45:41.944397Z"Georgiou, Dimitrios N."https://www.zbmath.org/authors/?q=ai:georgiou.dimitrios-n"Megaritis, Athanasios C."https://www.zbmath.org/authors/?q=ai:megaritis.athanasios-c"Özçağ, Selma"https://www.zbmath.org/authors/?q=ai:ozcag.selmaSummary: We study several kinds of statistical convergence of sequences of functions with values in semi-uniform spaces. Particularly, we generalize to statistical convergence the classical results of C. Arzelà, Dini and P. S. Alexandroff, as well as their statistical versions studied in [\textit{A. Caserta} et al., Abstr. Appl. Anal. 2011, Article ID 420419, 11 p. (2011; Zbl 1242.40003); Appl. Math. Lett. 25, No. 10, 1447--1451 (2012; Zbl 1255.54010)].Probabilistic approach spaces.https://www.zbmath.org/1463.540172021-07-26T21:45:41.944397Z"Jäger, Gunther"https://www.zbmath.org/authors/?q=ai:jager.guntherThe author studies a generalisation of Lowen's approach spaces. Given a point \(p\in S\) and a subset \(A\subseteq S\), a distribution function \(\delta(p,A)\) is assigned: its value at \(x\), \(\delta(p,A)(x)\), is interpreted as the probability that the distance of \(p\) from \(A\) is less than \(x\). The author introduces suitable axioms and shows that the resulting category is isomorphic to the category of left-continuous probabilistic topological convergence spaces and, as a consequence, is a topological category. The category of Lowen's approach spaces is isomorphic to a simultaneously bireflexive and bicoreflexive subcategory; he also shows that the category of quasi-metric spaces is isomorphic to a bicoreflexive subcategory of the category of probabilistic aproach spaces.The research of \(G\)-limit point set and \(G\)-chain equivalence sethttps://www.zbmath.org/1463.540182021-07-26T21:45:41.944397Z"Ji, Zhanjiang"https://www.zbmath.org/authors/?q=ai:ji.zhanjiang"Shi, Wei"https://www.zbmath.org/authors/?q=ai:shi.weiSummary: According to the definition of limit point and chain equivalence point in the metric space, we give the concepts of \(G\)-limit point and \(G\)-chain equivalence point and study their dynamical property in the metric \(G\)-space. We get some results about \(G\)-limit point and \(G\)-chain equivalence point. These results enrich the theory of \(G\)-limit point and \(G\)-chain equivalence point in the metric \(G\)-space.Resolvability in c.c.c. generic extensions.https://www.zbmath.org/1463.540192021-07-26T21:45:41.944397Z"Soukup, Lajos"https://www.zbmath.org/authors/?q=ai:soukup.lajos"Stanley, Adrienne"https://www.zbmath.org/authors/?q=ai:stanley.adrienne-mSummary: Every crowded space \(X\) is \(\omega\)-resolvable in the c.c.c. generic extension \(V^{\operatorname{Fn}(|X|,2)}\) of the ground model.
We investigate what we can say about \(\lambda\)-resolvability in c.c.c. generic extensions for \(\lambda >\omega\).
A topological space is \textit{monotonically} \(\omega_1\)-\textit{resolvable} if there is a function \(f:X\to\omega_1\) such that \[ \{x\in X:f(x)\geq \alpha\}\subset^{dense}X \] for each \(\alpha <\omega_1\).
We show that given a \(T_1\) space \(X\) the following statements are equivalent:\begin{enumerate}\item[(1)]\(X\) is \(\omega_1\)-resolvable in some c.c.c. generic extension;\item[(2)]\(X\) is monotonically \(\omega_1\)-resolvable;\item[(3)]\(X\) is \(\omega_1\)-resolvable in the Cohen-generic extension \(V^{\operatorname{Fn}(\omega_1,2)}\).\end{enumerate}
We investigate which spaces are monotonically \(\omega_1\)-resolvable. We show that if a topological space \(X\) is c.c.c., and \(\omega_1\leq\Delta(X)\leq |X|<\omega_{\omega}\), where \(\Delta(X) = \min\{ |G|:G\neq\emptyset \text{ open}\}\), then \(X\) is monotonically \(\omega_1\)-resolvable.
On the other hand, it is also consistent, modulo the existence of a measurable cardinal, that there is a space \(Y\) with \(|Y|=\Delta(Y)=\aleph_\omega\) which is not monotonically \(\omega_1\)-resolvable.
The characterization of \(\omega_1\)-resolvability in c.c.c. generic extension raises the following question: is it true that crowded spaces from the ground model are \(\omega\)-resolvable in \(V^{\operatorname{Fn}(\omega ,2)}\)?
We show that (i) if \(V=L\) then every crowded c.c.c. space \(X\) is \(\omega\)-resolvable in \(V^{\operatorname{Fn}(\omega,2)}\), (ii) if there are no weakly inaccessible cardinals, then every crowded space \(X\) is \(\omega\)-resolvable in \(V^{\operatorname{Fn}(\omega_1,2)}\).
Moreover, it is also consistent, modulo a measurable cardinal, that there is a crowded space \(X\) with \(|X|=\Delta(X)=\omega_1\) such that \(X\) remains irresolvable after adding a single Cohen real.On topological properties of generalized rough multisetshttps://www.zbmath.org/1463.540202021-07-26T21:45:41.944397Z"Abo-Tabl, El-Sayed A."https://www.zbmath.org/authors/?q=ai:abo-tabl.el-sayed-aSummary: Rough set theory is a powerful mathematical tool for dealing with inexact, uncertain or vague information. The core concept of rough set theory are information systems and approximation operators of approximation spaces. In this paper, we study the relationships between mset relations and mset topology. Moreover, this paper concerns generalized mset approximation spaces via topological methods and studies topological properties of rough msets. Classical compactness and connectedness for M-topological spaces are extended to generalized mset approximation spaces. Also, some properties of M-topological spaces induced by reflexive mset relation and some properties of M-topological spaces induced by tolerance mset relation are investigated.Three new weaker notions of fuzzy open sets and related covering conceptshttps://www.zbmath.org/1463.540212021-07-26T21:45:41.944397Z"Al Ghour, Samer H."https://www.zbmath.org/authors/?q=ai:al-ghour.samer-hamedSummary: A subset \(A\) of an ordinary topological space \((X,T)\) is \(\omega\)-open (resp. \(\mathcal{N}\)-open) if for each \(x\in A\), there exists \(U\in T\) such that \(x\in U\) and \(U-A\) is countable (resp. finite). In this work, we extend \(\omega\)-open and \(\mathcal{N}\)-open notions to include \(L\)-topological spaces, where \(L\) is an F-lattice, and we introduce a third notion of \(L\)-sets weaker than both of them. For a given \(L\)-topological space, the new notions give us three new finer \(L\)-topological spaces, which can help us to increase our understanding of this \(L\)-topological space. By means of these new notions in \(L\)-topological spaces, several types Chang's compactness, and Wong's Lindelöfness will be introduced. We make many comparisons between the new notions, and between these notions and some other related concepts. Several characterizations of the new concepts are given and two characterizations of Wong's Lindelöfness concept are given.On several types of continuity and irresoluteness in \(L\)-topological spaceshttps://www.zbmath.org/1463.540222021-07-26T21:45:41.944397Z"Al Ghour, Samer H."https://www.zbmath.org/authors/?q=ai:al-ghour.samer-hamedSummary: We use the concepts of \(\omega\)-open \(L\)-sets, \(\mathcal{N}\)-open \(L\)-sets and \(\mathcal{D}\)-open \(L\)-sets to define several new types of continuity or irresoluteness in \(L\)-topological spaces. Several results are given. In particular, decomposition theorems of the new irresoluteness concepts are introduced.Compactness in soft \(S\)-metric spaceshttps://www.zbmath.org/1463.540232021-07-26T21:45:41.944397Z"Aras, Cigdem Gunduz"https://www.zbmath.org/authors/?q=ai:aras.cigdem-gunduz"Bayramov, Sadi"https://www.zbmath.org/authors/?q=ai:bayramov.sadi-a"Cafarli, Vefa"https://www.zbmath.org/authors/?q=ai:cafarli.vefaSummary: The first aim of this paper is to contribute for investigating on soft \(S\)-metric space which is based on soft points of soft sets and to prove some important theorems on sequential compact and totally bounded in soft \(S\)-metric space. Moreover, we introduce soft uniformly continuous mapping and examine some of its properties.On multiset relations and factor multigroupshttps://www.zbmath.org/1463.540242021-07-26T21:45:41.944397Z"Awolola, J. A."https://www.zbmath.org/authors/?q=ai:awolola.johnson-aderemiSummary: Crisp congruence relations on groups are very well known. This paper attempts to define factor multigroups by using the proposed multiset relations in this study and prove some basic properties.A new form of fuzzy compactnesshttps://www.zbmath.org/1463.540252021-07-26T21:45:41.944397Z"Dapke, S. G."https://www.zbmath.org/authors/?q=ai:dapke.s-g"Aage, C. T."https://www.zbmath.org/authors/?q=ai:aage.chintaman-tukaram"Sahnke, J. N."https://www.zbmath.org/authors/?q=ai:sahnke.j-nSummary: The notion of \(\beta S^*\)-compactness is introduced by \textit{I. M. Hanafy} [J. Nonlinear Sci. Appl. 2, No. 1, 27--37 (2009; Zbl 1168.54303)]. In this paper we introduced the notion of \(\alpha S^*\)-compactness in \(L\)-fuzzy topological spaces based on \(\alpha\)-compactness. We give some characterizations of \(\alpha S^*\)-compactness and some of its topological properties are discussed.Fuzzy gp*-closed sets in fuzzy topological spacehttps://www.zbmath.org/1463.540262021-07-26T21:45:41.944397Z"Habib, Firdose"https://www.zbmath.org/authors/?q=ai:habib.firdose"Moinuddin, Khaja"https://www.zbmath.org/authors/?q=ai:moinuddin.khajaSummary: In this paper fuzzy gp*-closed sets, fuzzy gp* continuous functions, fuzzy gp*-irresolute functions, fuzzy gp*-connectedness and fuzzy T*gp-space are introduced and also their relation with some other fuzzy sets and some of their properties are investigated.Topological structures based on interval-valued setshttps://www.zbmath.org/1463.540272021-07-26T21:45:41.944397Z"Kim, J."https://www.zbmath.org/authors/?q=ai:kim.jonghan|kim.jong-geun|kim.jin-won|kim.jeong-hee|kim.junki|kim.jang-sub|kim.juyeon|kim.junsoo|kim.jong-in|kim.jaeuk|kim.jeong-tae|kim.junghi|kim.janghan|kim.jun-yeol|kim.jaegu|kim.jaewan|kim.jungeun|kim.jaehun|kim.junil|kim.jinsub|kim.junkon|kim.jinmyong|kim.jung-il|kim.jigu|kim.jong-jean|kim.jin-weon|kim.jai-hyun|kim.ju-kyong|kim.jihyun|kim.jangho|kim.jinhong|kim.jongkyu|kim.jin-gi|kim.jaemin|kim.ji-chul|kim.jin-baek|kim.jungon|kim.jongheon|kim.jongsung|kim.jae-kyoon|kim.jiseob|kim.ji-uk|kim.jae-jin|kim.jinheum|kim.jinsu|kim.jeong-kyun|kim.jae-hean|kim.jong-myon|kim.jinhyo|kim.jong-young|kim.jong-kwan|kim.junmo|kim.jihwan|kim.jai-hoon|kim.joung-dong|kim.jinmin|kim.jinil|kim.jongkil|kim.jun-kyo|kim.jaewon|kim.jane-i|kim.jerim|kim.jungduk|kim.jae-gyeom|kim.joongol|kim.jinkyu|kim.ju-min|kim.jongkwang|kim.jeongsim|kim.jaeyoel|kim.jin-soo|kim.ji-a|kim.jaedoek|kim.junhan|kim.ji-yu|kim.jongyoo|kim.juhyuk|kim.jwa-k|kim.jeong-ran|kim.jongho|kim.joonki|kim.jong-bum|kim.jiseok|kim.ji-sok|kim.jeongnim|kim.jaemyoung|kim.joonil|kim.jongtack|kim.jang-kyo|kim.jihan|kim.junhyeok|kim.jeong-sik|kim.jae-moung|kim.jungwook|kim.jaeyong|kim.jung-kuk|kim.jang-dae|kim.jin-song|kim.ju-sung|kim.jang-ho-robert|kim.joonsuk|kim.jongseong|kim.jung-bin|kim.joung-kook|kim.jinman|kim.jungdae|kim.jesung|kim.jeesun|kim.jung-sook|kim.jang-whan|kim.jaihie|kim.jeongmin|kim.jinwoong|kim.jaekwon|kim.joohwan|kim.jae-seung|kim.jee-soo|kim.jeeyeon|kim.jong-sung|kim.ju-hong|kim.jeungseop|kim.jin-seon|kim.jung-gu|kim.jeong-suk|kim.jinmi|kim.jehpill|kim.jong-myoung|kim.jin-yeub|kim.jeenu|kim.jong-uhn|kim.jaewoo|kim.junseong|kim.jaehoon|kim.jaehoo-park|kim.ji-young.1|kim.jeong-phill|kim.jongmin|kim.jane-jin|kim.jeongjin|kim.jeong-san|kim.jae-yun|kim.jongsun|kim.jee-seon|kim.jeongbae|kim.joondong|kim.jin-gon|kim.ju-seon|kim.jeonghun|kim.junehyung|kim.jewoo|kim.jin-yee|kim.jeong-ah|kim.jae-ryong|kim.ju-pil|kim.joonpyo|kim.jaechil|kim.jinbai|kim.junbeom|kim.jong-seop|kim.jin-yong|kim.jung-ok|kim.jungho|kim.jongsik|kim.jiwhan|kim.jeon-g|kim.jong-bong|kim.jongjoo|kim.jae-kyoung|kim.jea-soo|kim.junbeum|kim.jae-gang|kim.jeongyong|kim.jaeho|kim.jung-ug|kim.ji-eun|kim.jong-yong|kim.jihun|kim.jaedeok|kim.jahwan|kim.jihoon|kim.jon-lark|kim.jong-gyoon|kim.jindae|kim.joon-seok|kim.janet-s|kim.jaehyeong|kim.jae-joo|kim.ji-hyung|kim.jaiseung|kim.joohyung|kim.jueun|kim.jae-hyung|kim.jong-nam|kim.jeong-sik.1|kim.jinki|kim.jeong-soon|kim.jayoun|kim.jongpil|kim.jaehong|kim.jimin|kim.jinbang|kim.jong-hae|kim.jungchul|kim.jangyeop|kim.jin-ran|kim.jaeyeon|kim.jeong-hoon|kim.joon-sik|kim.joong-hoon|kim.jong-kook|kim.jong-chan|kim.jongwook|kim.joohee|kim.jung-ha|kim.juwan|kim.je-seok|kim.jong-rip|kim.jong-heong|kim.jong-hoon|kim.jin-kon|kim.jin-seob|kim.ji-yoon|kim.joocheol|kim.jeom-keun|kim.jayme|kim.jong-ryul|kim.jee-hyoun|kim.jee-hyub|kim.ju-yeong|kim.jae-kyu|kim.joohyun|kim.jeongseob|kim.jongsu|kim.jung-rim|kim.jong-uhm|kim.jinoh|kim.jan-t|kim.joohong|kim.juyoung|kim.jungkwon|kim.ju-myung|kim.jae-yo|kim.joongbae|kim.joonshik|kim.jangseong|kim.jeong-heon|kim.je-guk|kim.jeong-oun|kim.jaeseon|kim.jongman|kim.jibum|kim.jiwon|kim.jongphil|kim.jiseung|kim.jung-jin|kim.jane-paik|kim.jaehee-h|kim.junhyuk|kim.junhyong|kim.junseok|kim.ji-yeun|kim.jeong-yoo|kim.ju-han|kim.jung-in|kim.jongjin|kim.jai-heui|kim.jaesung|kim.jun-o|kim.jungdo|kim.joong-han|kim.jinhyon|kim.jin-gyo|kim.junhui|kim.jonghoek|kim.jungjoon|kim.june-hoan|kim.jisoo|kim.jae-in|kim.jungmin|kim.jinkook|kim.jung-ae|kim.jinwoo|kim.jin-chun|kim.jongbae|kim.jiho|kim.jae-duck|kim.jongwon|kim.jongchon|kim.jong-kyoung|kim.jeehoon|kim.jeong-chul|kim.jinhak|kim.junguk-l|kim.jaemoon|kim.jee-hye|kim.jin-gyoung|kim.jungsil|kim.ju-lee|kim.jaekwan|kim.jun-suk|kim.jeonglae|kim.jeng-in|kim.jin-dong|kim.jaehwan|kim.jeong-beom|kim.jongtae|kim.jung-hoon|kim.jaeseok|kim.jae-hyun|kim.jaewoong|kim.junae|kim.jongyoon|kim.juhyung|kim.jinhyung|kim.jong-ah|kim.jae-eun|kim.jong-uk|kim.jae-kyeong|kim.jong-myung|kim.jung-hyun|kim.jinkoo|kim.jonghyun|kim.jong-chol|kim.junwoo|kim.jeong-ryeol|kim.jeonghwan|kim.james-j|kim.jinam|kim.jinha|kim.jae-eui|kim.jong-gun|kim.jongrae|kim.jinsung|kim.jung-yup|kim.john-y|kim.jesse|kim.ju-hee|kim.jae-chun|kim.joo-mok|kim.jihong|kim.joo-bong|kim.jaehyoun|kim.jinmee|kim.juntae|kim.june-gi|kim.jinsang|kim.jinill|kim.jungsup|kim.jinbeom|kim.jae-kwang|kim.jongeun|kim.jihn-e|kim.jong-pal|kim.jeong-uk|kim.jake|kim.jinseung|kim.jae-do|kim.joongnyon|kim.joo-han|kim.jeunghyun|kim.jinhyuk|kim.joonoh|kim.jonghyuk|kim.jong-gurl|kim.jong-yun|kim.jungsun|kim.jinmook|kim.jinsuk|kim.jaejik|kim.jung-yub|kim.jiyean|kim.jaywoo|kim.jee-hyun|kim.jung-yong|kim.joonoo|kim.jung-sub|kim.jinseok|kim.june-young|kim.jongwan|kim.jae-young|kim.joo-sung|kim.jin-hee|kim.junhong|kim.jong-youl|kim.jaegil|kim.jeongeun|kim.jihye|kim.jeong-yeol|kim.jieon|kim.ju-hyun|kim.jitae|kim.jinsoo|kim.jong-kyu|kim.junhyun|kim.jongwoo|kim.jai-sam|kim.jeankyung|kim.jinhyun|kim.jaeil|kim.jong-hwan|kim.junghan|kim.jong-ok|kim.joonhyung|kim.jeongho|kim.junghwan|kim.jin-a|kim.jang-hoon|kim.jeomgoo|kim.joungyoun|kim.jeongsoo|kim.jonghyeon|kim.jin-hoon|kim.jeounghoon|kim.jung-seek|kim.jae-yearn|kim.jay-jung|kim.jeongook|kim.jung-kon|kim.jerry|kim.joonmo|kim.jeongsol|kim.jeong-gyoo|kim.jin-j|kim.jaeboo|kim.jin-hong|kim.jung-bae|kim.jong-hun|kim.jinseog|kim.jiwoon|kim.jin-yeon-f|kim.jinwook|kim.jik-soo|kim.joontae|kim.jayeon|kim.jungsoo|kim.jimyeong|kim.jongik|kim.ji-yeoun|kim.jangil|kim.jeong-han|kim.jungwon|kim.jinhwa|kim.jaewook|kim.jong-kyou|kim.jaehwang|kim.jeongwon|kim.junhyeung|kim.junghwa|kim.jong-chul|kim.jae-hak|kim.jae-jun|kim.joong-jae|kim.jeongguk|kim.jongseok|kim.joong-ho|kim.joonho|kim.jinho|kim.jeonghyun|kim.junggon|kim.jong-shik|kim.jooseuk|kim.john-j|kim.jinyoung|kim.jin-ok|kim.junha|kim.jason-z|kim.ji-hee|kim.jeong-il|kim.junhwan|kim.jong-hyouk|kim.jung-su|kim.jungkyu|kim.jeong-hyuk|kim.ji-hyun|kim.joo-young|kim.jong-soo|kim.jewan|kim.jong-soon|kim.joongkyu|kim.ji-young|kim.jaeyoon|kim.jae-gon|kim.jaekwang|kim.jin-gyun|kim.jeongsu|kim.jaeman|kim.jeongwoo|kim.jeong-bon|kim.ji-yeon|kim.jeongkyu|kim.jung-kyung|kim.jaesoo|kim.jong-woong|kim.jin-hwan|kim.jang-soo|kim.jiwoong|kim.jeehong|kim.jisu|kim.jin-yul|kim.jihie|kim.jaeheon|kim.ji-youp|kim.jong-moon|kim.jeong-gyun|kim.jae-cheol|kim.jungkee|kim.jinwhan|kim.jungwoo|kim.ja-young|kim.jong-geon|kim.jaegyun|kim.jae-kyung|kim.jingu|kim.jintae|kim.junho|kim.jangyoung|kim.jeong-rae|kim.joseph-hyun-tae"Jun, Y. B."https://www.zbmath.org/authors/?q=ai:yun.y-b|jun.young-bae|jun.young-bea|jun.young-bi"Lee, J. G."https://www.zbmath.org/authors/?q=ai:lee.jong-geol|lee.jong-gu|lee.jung-gon|lee.jeh-gwon|lee.jin-gyu|lee.jong-gi|lee.jae-gil|lee.jang-gyu|lee.jeong-gon|lee.jeong-gyu|lee.jianguo|lee.joong-geun"Hur, K."https://www.zbmath.org/authors/?q=ai:hur.kwangho|hur.kul|hur.kyeonSummary: In this paper, we define an interval-valued set and an interval-valued (vanishing) point, and study some of their properties. In particular, we get the characterization of inclusions, intersections and unions of interval-valued sets. Also, we deal with some properties of the images and the preimages under a mapping. Moreover, we introduce the concept of interval-valued ideals and some of its properties. Next, we define an interval-valued topology, an interval-valued base [rep. subbase] and an interval-valued neighborhood, and find their various properties. Finally, we define an interval-valued closure [resp. interior] and obtain some of each properties. Moreover, we show that that there is a unique IVT for interval-valued interior [resp. closure] operators.The category of hesitant \(H\)-fuzzy setshttps://www.zbmath.org/1463.540282021-07-26T21:45:41.944397Z"Kim, J."https://www.zbmath.org/authors/?q=ai:kim.junhui|kim.jong-youl|kim.jeunghyun"Jun, Y. B."https://www.zbmath.org/authors/?q=ai:jun.young-bae"Lim, P. K."https://www.zbmath.org/authors/?q=ai:lim.pyung-ki"Lee, J. G."https://www.zbmath.org/authors/?q=ai:lee.jong-geol|lee.jeong-gon"Hur, K."https://www.zbmath.org/authors/?q=ai:hur.kulSummary: We redefine the hesitant fuzzy empty set, the hesitant fuzzy whole set, the intersection and the union of two hesitant fuzzy sets, and prove that the family \(HS(X)\) of all hesitant fuzzy sets in a set \(X\) is a Boolean algebra. Next, we introduce the category \(\mathbf{HSet}(H)\) consisting of hesitant \(H\)-fuzzy spaces and preserving mappings between them and study the category \(\mathbf{HSet}(H)\) in the sense of a topological universe and prove that
it is Cartesian closed over \textbf{Set}, where \textbf{Set} denotes the category consisting of ordinary sets and ordinary mappings between them.\((L, \ast)\)-filters and \((L, \ast, \odot)\)-limit spaceshttps://www.zbmath.org/1463.540292021-07-26T21:45:41.944397Z"Ko, Jung Mi"https://www.zbmath.org/authors/?q=ai:ko.jung-mi"Kim, Yong Chan"https://www.zbmath.org/authors/?q=ai:kim.yong-chan.1Summary: In this paper, we introduce the notion of the \((L,{\ast},{\odot})\)-limit spaces and investigate the relations \((L,{\ast},{\odot})\)-limit spaces and \((L,{\ast})\)-filters on ecl-premonoid. We give their examples.The balanced Q-neighborhood systems of zero element in I-fuzzy topological vector spaceshttps://www.zbmath.org/1463.540302021-07-26T21:45:41.944397Z"Li, Hui"https://www.zbmath.org/authors/?q=ai:li.hui|li.hui.2|li.hui.1|li.hui.3|li.hui.5|li.hui.4"Wang, Ruiying"https://www.zbmath.org/authors/?q=ai:wang.ruiying"Geng, Jun"https://www.zbmath.org/authors/?q=ai:geng.junSummary: In this paper, we introduce the concept of I-fuzzy topological vector space, and use semantic method of continuous-valued logic to research the properties of Q-neighborhood systems of discretional fuzzy point in I-fuzzy topological vector spaces. Next, we discuss the structures and properties of the balanced Q-neighborhood systems of zero element. Finally, the characterizing theorem of the balanced Q-neighborhood systems of zero element for I-fuzzy topological vector spaces is established.The distance of fuzzy closure sets in fuzzy sets spacehttps://www.zbmath.org/1463.540312021-07-26T21:45:41.944397Z"Li, Yanhong"https://www.zbmath.org/authors/?q=ai:li.yanhongSummary: Fuzzy closure set is a basic concept in fuzzy system theory, and it has important applications in fuzzy topology. In this paper, the definition of fuzzy closure set is given by means of the decomposition theorem, and the distance formula of general fuzzy sets is obtained by using Hausdorff metric. Secondly, the distance properties between a classical set and its closure are discussed on the basis of one-dimensional Hausdorff metric. Finally, the distance properties of fuzzy closure sets are given by the cut set formula of fuzzy closure sets under certain restrictions.Fuzzifying sp-topological space and the topological properties of category FfSPTophttps://www.zbmath.org/1463.540322021-07-26T21:45:41.944397Z"Meng, Liyuan"https://www.zbmath.org/authors/?q=ai:meng.liyuan"Geng, Jun"https://www.zbmath.org/authors/?q=ai:geng.jun"Wang, Ruiying"https://www.zbmath.org/authors/?q=ai:wang.ruiyingSummary: In this paper, based on the continuous logic value semantics, we study the fuzzifying sp-topological space, discuss the properties of fuzzifying sp-open sets, sp-neighborhood, sp-closure and sp-interior and give the concept of fuzzifying sp-continuous mapping. On this basis, we introduce the category FSPTop. Furthermore, we prove that the category FSPTop is the topological category on the category set.Topological properties of the category \(\textbf{FSCPTop}\)https://www.zbmath.org/1463.540332021-07-26T21:45:41.944397Z"Meng, Liyuan"https://www.zbmath.org/authors/?q=ai:meng.liyuan"Wang, Ruiying"https://www.zbmath.org/authors/?q=ai:wang.ruiyingSummary: Based on the continuous logic value semantics, we introduced the fuzzifying \(scp\)-open sets, defined the concept of fuzzifying \(scp\)-topological space and fuzzifying \(scp\)-continuous mapping. Furthermore, we discussed the category \(\textbf{FSCPTop}\) and proved that the category \(\textbf{FSCPTop}\) was the topological category on the category \(\textbf{Set}\).On fuzzy \(SU\)-ideal topological structurehttps://www.zbmath.org/1463.540342021-07-26T21:45:41.944397Z"Muralikrishna, P."https://www.zbmath.org/authors/?q=ai:muralikrishna.prakasam"Vijayan, D."https://www.zbmath.org/authors/?q=ai:viyayan.duraisamySummary: This paper discuss fuzzy \(SU\)-ideal topological structure on \(SU\)-algebras, by connecting the two notions \(SU\)-algebras and fuzzy tpology.Some properties of fuzzifying scp-topological spacehttps://www.zbmath.org/1463.540352021-07-26T21:45:41.944397Z"Pi, Jiandong"https://www.zbmath.org/authors/?q=ai:pi.jiandong"Meng, Liyuan"https://www.zbmath.org/authors/?q=ai:meng.liyuan"Wang, Ruiying"https://www.zbmath.org/authors/?q=ai:wang.ruiyingSummary: Based on the continuous logic value semantics, this paper studies the fuzzifying scp-topological space, and discusses the properties of scp-open sets, scp-neighborhood, scp-closure and scp-interior. Furthermore, we give the definition of fuzzifying scp-continuous mapping.Some new properties on soft topological spaceshttps://www.zbmath.org/1463.540362021-07-26T21:45:41.944397Z"Saleh, S."https://www.zbmath.org/authors/?q=ai:saleh.s-q|saleh.shokrya|saleh.siti-hidayah-muhad|saleh.s-v|saleh.samera-m|saleh.shanti-faridah|saleh.sagvan|saleh.sami|saleh.sahar-mohamad|saleh.s-a|saleh.saad-jSummary: In this paper, we introduce and study some new soft properties namely, soft \(R_0\) and soft \(R_1\) (\(SR_i\), for short \(i=0,1\)) by using the concept of distinct soft points and we obtain some of their properties. We show how they relate to some soft separation axioms in [\textit{O. Tantawy} et al., ibid. 11, No. 4, 511--525 (2016; Zbl 1347.54024)]. Also we, show that the properties \(SR_0\), \(SR_1\) are special cases of soft regularity. We further, show that in the case of soft compact spaces, \(SR_1\) is equivalent to soft regularity. Finally, the relations between these properties in soft topologies and that in crisp topologies are studied. Moreover, some counterexamples are given.New investigation of Ćirić type fuzzy soft contractive mapping in fuzzy soft metric spaceshttps://www.zbmath.org/1463.540372021-07-26T21:45:41.944397Z"Sayed, A. F."https://www.zbmath.org/authors/?q=ai:sayed.a-f"Ahmad, Jamshaid"https://www.zbmath.org/authors/?q=ai:ahmad.jamshaid"Hussain, Aftab"https://www.zbmath.org/authors/?q=ai:hussain.aftabSummary: This paper is view to introduce the notion of fuzzy soft metric space with some of its important properties. In this way we introduce and investigate Ćirić type fuzzy soft contractive mappings to establish fixed point theorem of the mapping in the context of fuzzy soft metric spaces.On pairwise fuzzy semi weakly Volterra spaceshttps://www.zbmath.org/1463.540382021-07-26T21:45:41.944397Z"Thangaraj, Ganesan"https://www.zbmath.org/authors/?q=ai:thangaraj.ganesan"Chandiran, Venkattappan"https://www.zbmath.org/authors/?q=ai:chandiran.venkattappanSummary: In this paper, by using pairwise fuzzy semi \(G_\delta\)-sets and pairwise fuzzy semi dense sets, the concept of pairwise fuzzy semi weakly Volterra space is introduced and studied. Example is given for pairwise fuzzy semi weakly Volterra spaces. Several characterizations of pairwise fuzzy semi weakly Volterra spaces are also given in this paper. The inter-relations between pairwise fuzzy semi Volterra and pairwise fuzzy semi weakly Volterra spaces, are also established.Some remarks on fuzzy globally disconnected spaceshttps://www.zbmath.org/1463.540392021-07-26T21:45:41.944397Z"Thangaraj, Ganesan"https://www.zbmath.org/authors/?q=ai:thangaraj.ganesan"Muruganantham, Subban"https://www.zbmath.org/authors/?q=ai:muruganantham.subbanSummary: In this paper, several characterizations of fuzzy globally disconnected spaces, are established. By means of fuzzy globally disconnectedness, conditions for fuzzy topological spaces to become fuzzy Baire spaces, are established. The conditions under which fuzzy sets become fuzzy simply open sets and fuzzy residual sets, fuzzy somewhere dense sets, fuzzy dense sets become fuzzy open sets in fuzzy globally disconnected spaces, are also obtained.On fuzzy \(B^*\) setshttps://www.zbmath.org/1463.540402021-07-26T21:45:41.944397Z"Thangaraj, G."https://www.zbmath.org/authors/?q=ai:thangaraj.ganesan"Dharmasaraswathi, S."https://www.zbmath.org/authors/?q=ai:dharmasaraswathi.sSummary: In this paper, the concepts of fuzzy \(B^*\) sets in a fuzzy topological spaces are introduced and studied. Several characterizations of fuzzy \(B^*\) sets are established.On fuzzy maximal spaceshttps://www.zbmath.org/1463.540412021-07-26T21:45:41.944397Z"Thangaraj, G."https://www.zbmath.org/authors/?q=ai:thangaraj.ganesan"Lokeshwari, S."https://www.zbmath.org/authors/?q=ai:lokeshwari.sSummary: In this paper, a new class of topological spaces, called maximal spaces, is introduced by means of fuzzy submaximality and fuzzy extremally disconnectedness of fuzzy topological spaces. Several characterizations of fuzzy maximal spaces are established. It is established that fuzzy maximal spaces, are fuzzy nodec spaces and fuzzy irresolvable spaces and fuzzy maximal spaces are neither fuzzy Baire spaces nor fuzzy \(\beta\)-Baire spaces.A characterization of a fuzzy quasi-metric in terms of a family of quasi-metricshttps://www.zbmath.org/1463.540422021-07-26T21:45:41.944397Z"Tian, Keming"https://www.zbmath.org/authors/?q=ai:tian.keming"Wu, Jianrong"https://www.zbmath.org/authors/?q=ai:wu.jianrongSummary: This paper deals with the structure problem of a fuzzy quasi-metric space. After introducing the concept of the family of star quasi-metrics, a characterization of a fuzzy quasi-metric in terms of a quasi-metric family is given. That is, a function is a fuzzy quasi-metric if and only if it can be induced by a star quasi-metric family which is both increasing and upper semi-continuous.Locally \(Z\)-spaces and \(Z\)-continuous spaceshttps://www.zbmath.org/1463.540432021-07-26T21:45:41.944397Z"Xiong, Xianglong"https://www.zbmath.org/authors/?q=ai:xiong.xianglong"Xu, Xiaoquan"https://www.zbmath.org/authors/?q=ai:xu.xiaoquan.1|xu.xiaoquanSummary: In this paper, for a generalized subset system \(Z\), the concepts of locally \(Z\)-spaces and \(Z\)-continuous spaces are introduced, and some basic properties of the locally \(Z\)-spaces are discussed. Based on convergent nets, it is proved that a space \(X\) is a locally \(Z\)-space if and only if \(X\) is a \(Z\)-continuous space.Making holes in the cone, suspension and hyperspaces of some continua.https://www.zbmath.org/1463.540442021-07-26T21:45:41.944397Z"Anaya, José G."https://www.zbmath.org/authors/?q=ai:anaya.jose-g"Castañeda-Alvarado, Enrique"https://www.zbmath.org/authors/?q=ai:castaneda-alvarado.enrique"Fuentes-Montes de Oca, Alejandro"https://www.zbmath.org/authors/?q=ai:fuentes-montes-de-oca.alejandro"Orozco-Zitli, Fernando"https://www.zbmath.org/authors/?q=ai:orozco-zitli.fernandoA connected space is unicoherent if \(A\cap B\) is connected for every pair of closed connected subsets \(A\) and \(B\) whose union is \(Z\). A point \(z\) in a unicoherent space \(Z\) makes a hole in \(Z\) if \(Z\setminus\{z\}\) is connected and non-unicoherent.
In this paper the authors make a detailed study of the elements that make holes in cones, suspensions and some hyperspaces of continua. Besides showing general results related with this topic, they obtain the following interesting results.
- For a connected space \(Z\), no element of the suspension of \(Z\) makes a hole if and only if \(Z\) does not have cut points.
- For a finite graph \(G\), a characterization of the elements that make a hole in cone(\(G\)) is given.
- For a connected closed unicoherent \(n\)-manifold \(M\) with \(n>1\), no point makes a hole in cone(\(M\)).
- For a connected closed non-unicoherent \(n\)-manifold \(M\) with \(n>1\), the only point making a hole in cone(\(M\)) is the vertex of the cone.
- For a compactification \(X\) of the ray \([0,\infty)\), a characterization of points making a hole in cone(\(X\)) is given.
- For a generalized Warsaw circle \(X\), a characterization of the points making a hole in cone(\(X\)) is given.
- Partial results about elements making holes in the hyperspace \(C_{n}(X)\) of nonempty closed subsets with at most \(n\) components of a metric continuum \(X\) are given.
- Partial results about elements making holes in the hyperspace \(F_{n}(X)\) of nonempty subsets with at most \(n\) points of a metric continuum \(X\) are given.
The authors include the following conjectures:
- For \(n>1\), no element makes a hole in \(C_{n}([0,1])\).
- For \(n>3\), no element makes a hole in \(F_{n}([0,1])\).
Two final remarks.
Theorem 5.5, about hyperspaces which are cones, was published previously as Theorem 4, in the paper [\textit{A. Illanes} and \textit{V. Martínez-de-la-Vega}, Topology Appl. 228, 36--46 (2017; Zbl 1392.54017)].
The authors pretend to give an alternative proof, in Theorem 5.10, that if \(S^{1}\) is the unit circle in the plane, then \(C_{2}(S^{1})\setminus\{S^{1}\}\) is not unicoherent. As they mention, there are two previous proofs of this fact given by the reviewer in [Glas. Mat., III. Ser. 37, No. 2, 347--363 (2002; Zbl 1026.54009)] and [Quest. Answers Gen. Topology 22, No. 2, 117--130 (2004; Zbl 1065.54004)]. Their ``proof'' does not work since they make the common mistake of defining a function on the elements of \(C_{2}(S^{1})\) with exactly two components which cannot be continuously extended to the elements of \(C_{2}(S^{1})\) with exactly one component.On some properties of the hyperspace \(\theta (X)\) and the study of the space \(\downarrow \theta C(X)\)https://www.zbmath.org/1463.540452021-07-26T21:45:41.944397Z"Sen, R."https://www.zbmath.org/authors/?q=ai:sen.rajat|sen.rabindranath|sen.rohini|sen.ravindra|sen.ramdas|sen.rituparna|sen.rudra|sen.rituSummary: The aim of the paper is to first investigate some properties of the hyperspace \(\theta(X)\), and then in the next article it deals with some detailed study of a special type of subspace \(\downarrow\theta C(X)\) of the space \(\theta (X\times \mathbb{I})\).Continuous and homomorphism mapping of covering approximate spacehttps://www.zbmath.org/1463.540462021-07-26T21:45:41.944397Z"He, Jiali"https://www.zbmath.org/authors/?q=ai:he.jialiSummary: In this paper, some properties of covering approximate space are studied by general mapping, and some conclusions are proved. Then we define the continuous mapping and homeomorphism mapping of the covering space. At last, we study the properties of two covering approximate spaces under the condition of continuous mapping and homomorphism mapping. The classification of the approximate space provides a theoretical basis.On \(bg^{\mu}\)-closed maps and \(bg^{\mu}\)-homeomorphisms in supra topological spaceshttps://www.zbmath.org/1463.540472021-07-26T21:45:41.944397Z"Krishnaveni, K."https://www.zbmath.org/authors/?q=ai:krishnaveni.k"Janaki, K."https://www.zbmath.org/authors/?q=ai:janaki.kSummary: The aim of this paper, is to introduce a new class of set namely \(bg^\mu\)-closed maps and \(bg^\mu\)-homeomorphisms in supra topological spaces and study some of their properties. Using these new types of maps, several properties have been obtained.On generalized \(B^*\)-continuity, \(B^*\)-coverings and \(B^*\)-separationshttps://www.zbmath.org/1463.540482021-07-26T21:45:41.944397Z"Jain, Pankaj"https://www.zbmath.org/authors/?q=ai:jain.pankaj"Basu, Chandrani"https://www.zbmath.org/authors/?q=ai:basu.chandrani"Panwar, Vivek"https://www.zbmath.org/authors/?q=ai:panwar.vivekSummary: There are various generalizations of continuous functions in topological spaces and \(B^*\)-continuity is one of them which deals with the Baire property and denseness of the space. We have defined and discussed several properties and interrelations of some further generalizations of \(B^*\)-continuity, namely, contra \(B^*\)-continuity, slight \(B^*\)-continuity and weak \(B^*\)-continuity. We have also defined certain notions of generalized coverings and separations in terms of \(B^*\)-sets and studied the effect of generalized \(B^*\)-continuous functions on spaces having these covering and separation properties.On weakly \(e^*\)-open and weakly \(e^*\)-closed functionshttps://www.zbmath.org/1463.540492021-07-26T21:45:41.944397Z"Özkoc, M."https://www.zbmath.org/authors/?q=ai:ozkoc.murad"Erdem, S."https://www.zbmath.org/authors/?q=ai:erdem.sabri|erdem.sezer|erdem.serdar-suer|erdem.sadettinSummary: The aim of this paper is to introduce and study two new classes of functions called weakly \(e^*\)-open functions and weakly \(e^*\)-closed functions via the concept of \(e^*\)-open set defined by \textit{E. Ekici} [Math. Morav. 13, No. 1, 29--36 (2009; Zbl 1265.54072)]. The notions of weakly \(e^*\)-open and weakly \(e^*\)-closed functions are weaker than the notions of weakly \(\beta\)-open and weakly \(\beta\)-closed functions defined by \textit{M. Caldas} and \textit{G. Navalagi} [An. Ştiinţ. Univ. Al. I. Cuza Iaşi, Ser. Nouă, Mat. 49, No. 1, 115--128 (2003; Zbl 1059.54501)], respectively. Moreover, we investigate not only some of their fundamental properties, but also their relationships with other types of existing topological functions.\(\mathcal{C}\ \text m \alpha \text g\) continuous function in topological spaceshttps://www.zbmath.org/1463.540502021-07-26T21:45:41.944397Z"Kokilavani, V."https://www.zbmath.org/authors/?q=ai:kokilavani.v"Priyadarshini, S. Meena"https://www.zbmath.org/authors/?q=ai:priyadarshini.s-meenaSummary: In this paper, we introduce and investigate a new class of mappings namely contra mildly \(\alpha\) generalized continuous (briefly \(\mathcal C \ \text m \alpha \text g\) continuous) maps and discuss their relation between few existing contra continuous maps.Contra \(\mathcal{I}_{wg}\)-continuity in ideal spaceshttps://www.zbmath.org/1463.540512021-07-26T21:45:41.944397Z"Sangeethasubha, Vanangamudi"https://www.zbmath.org/authors/?q=ai:sangeethasubha.vanangamudi"Prabakaran, Thiruvalagu"https://www.zbmath.org/authors/?q=ai:prabakaran.thiruvalagu"Seenivasagan, Narayanasamy"https://www.zbmath.org/authors/?q=ai:seenivasagan.narayanasamy"Ravi, Ochadevar"https://www.zbmath.org/authors/?q=ai:ravi.ochadevarSummary: In this paper, the concepts of \(\mathcal{I}_{wg}\)-closed sets and \(\mathcal{I}_{wg}\)-open sets are introduced and they are used to define and investigate a new class of functions called contra \(\mathcal{I}_{wg}\)-continuous functions in ideal spaces. We discuss the relationships with some other related functions.The open-point and compact-open topology on \(C (X)\)https://www.zbmath.org/1463.540522021-07-26T21:45:41.944397Z"Peng, Liangxue"https://www.zbmath.org/authors/?q=ai:peng.liangxue"Sun, Yuan"https://www.zbmath.org/authors/?q=ai:sun.yuanSummary: In this note we define a new topology on \(C (X)\), the set of all real-valued continuous functions on a Tychonoff space \(X\). The new topology on \(C (X)\) is the topology having subbase open sets of both kinds: \([f,C,\varepsilon] = \{g \in C (X):|f(x)-g (x)|< \varepsilon\; {\mathrm{for\; every}}\; x \in C\}\) and \([U,r]^- = \{g \in C (X):g^{-1} (r) \cap U \ne\emptyset\}\), where \(f\in C (X)\), \(C\in K (X) = \{\text{nonempty compact subsets of } X\}\), \(\epsilon > 0\), while \(U\) is an open subset of \(X\) and \(r \in \mathbb{R}\). The space \(C (X)\) equipped with the new topology \(\mathcal{T}_{kh}\) which is stated above is denoted by \(C_{kh} (X)\). Denote \({X_0} = \{x\in X: x\; {\mathrm{is\; an\; isolated\; point\; of}}\; X\}\) and \({X_c} = \{x \in X: x\; {\mathrm{has\; a\; compact\; neighborhood\; in}}\; X\}\). We show that if \(X\) is a Tychonoff space such that \({X_0} = {X_c}\), then the following statements are equivalent: (1) \({X_0}\) is \({G_\delta}\)-dense in \(X\); (2) \({C_{kh}} (X)\) is regular; (3) \({C_{kh}} (X)\) is Tychonoff; (4) \({C_{kh}} (X)\) is a topological group. We also show that if \(X\) is a Tychonoff space such that \({X_0} = {X_c}\) and \({C_{kh}} (X)\) is regular space with countable pseudo-character, then \(X\) is \(\sigma\)-compact. If \(X\) is a metrizable hemicompact countable space, then \({C_{kh}} (X)\) is first countable.On \(z^c\)-ideals of topological spacehttps://www.zbmath.org/1463.540532021-07-26T21:45:41.944397Z"Aral, Zohreh"https://www.zbmath.org/authors/?q=ai:aral.zohrehSummary: We define the concept of \(z^c\)-ideal by use the complement of the zero-sets on topological space \(X\) and obtain some applications of them on the ring of continuous functions. We also study some related properties of them.\(z^\circ\)-filters and related ideals in \(C(X)\)https://www.zbmath.org/1463.540542021-07-26T21:45:41.944397Z"Mohamadian, Rostam"https://www.zbmath.org/authors/?q=ai:mohamadian.rostamSummary: In this article we introduce the concept of \(z^\circ\)-filter on a topological space \(X\). We study and investigate the behavior of \(z^\circ\)-filters and compare them with corresponding ideals, namely, \(z^\circ\)-ideals of \(C(X)\), the ring of real-valued continuous functions on a completely regular Hausdorff space \(X\). It is observed that \(X\) is a compact space if and only if every \(z^\circ\)-filter is ci-fixed. Finally, by using \(z^\circ\)-ultrafilters, we prove that any arbitrary product of i-compact spaces is i-compact.On the mappings \(\mathcal{Z}_A\) and \(\Im_A\) in intermediate rings of \(C(X)\).https://www.zbmath.org/1463.540552021-07-26T21:45:41.944397Z"Parsinia, Mehdi"https://www.zbmath.org/authors/?q=ai:parsinia.mehdiSummary: In this article, we investigate new topological descriptions for two well-known mappings \(\mathcal{Z}_A\) and \(\Im_A\) defined on intermediate rings \(A(X)\) of \(C(X)\). Using this, coincidence of each two classes of \(z\)-ideals, \(\mathcal{Z}_A\)-ideals and \(\Im_A\)-ideals of \(A(X)\) is studied. Moreover, we answer five questions concerning the mapping \(\Im_A\) raised in [\textit{J. Sack} and \textit{S. Watson}, Topol. Proc. 43, 69--82 (2014; Zbl 1279.54016)].Weak \(R\)-spaces and uniform limit of sequences of the first Baire class functionshttps://www.zbmath.org/1463.540562021-07-26T21:45:41.944397Z"Karlova, Olena"https://www.zbmath.org/authors/?q=ai:karlova.olena|karlova.olena-o"Lukan', Mykhaylo"https://www.zbmath.org/authors/?q=ai:lukan.mykhayloSummary: A function \(f : X\to Y\) between topological spaces \(X\) and \(Y\) is called a Baire-one function, if there exists a sequence of continuous functions \(f_n : X\to Y\) such that \(\lim_{n\to\infty} f_n(x)=f(x)\) for every \(x\in X\). We denote the collection of all Baire-one functions between \(X\) and \(Y\) by \(B_1(X,Y)\). It is know that the class \(B_1(\mathbb{R},\mathbb{R})\) is closed under uniform limits. \textit{O. O. Karlova} and \textit{V. V. Mykhajlyuk} proved in [Ukr. Mat. Zh. 58, No. 4, 568--572 (2006; Zbl 1122.54011); translation in Ukr. Math. J. 58, No. 4, 640--644 (2006)] that the class \(B_1(X,Y)\) is closed under uniform limits if \(X\) is a topological space and \(Y\) is metrizable path-connected and locally path-connected space. From the other hand, it was shown that there exist a path-connected (but not locally path-connected) subset \(Y\subset \mathbb{R}^2\) and a sequence of Baire-one functions \(f_n : [0,1]\to Y\) which tends uniformly to a function \(f : [0,1]\to Y\) such that \(f\) does not belong to the first Baire class. Therefore, it is actual to study spaces \(Y\) for which the class \(B_1(X, Y)\) is closed under uniform limits. The notion of an \(R\)-space was introduced by \textit{O. O. Karlova} [Nauk. Visn. Chernivets'kogo Univ., Mat. 239, 59--65 (2005; Zbl 1098.54014)], who proved that if \(Y\) is an \(R\)-space, then \(B_1(X, Y)\) is closed under uniform limits for arbitrary topological space \(X\). Unfortunately, the definition of \(R\)-space is rather strong in order to include many curves on the plane. We introduce a class of weak \(R\)-spaces which includes convex subsets of normed spaces and some other curves than a circle on the plane, and prove that the uniform limit \(f\) of a sequence of Baire-one functions \(f_n : X\to Y\) between a topological spaces \(X\) and a weak \(R\)-space \(Y\) belongs to the first Baire class.A new class of fractional type set-valued functionshttps://www.zbmath.org/1463.540572021-07-26T21:45:41.944397Z"Orzan, Alexandru"https://www.zbmath.org/authors/?q=ai:orzan.alexandruSummary: The so-called ratios of affine functions, introduced by \textit{U. G. Rothblum} [Math. Program. 32, 357--365 (1985; Zbl 0571.90070)] in the framework of finite-dimensional Euclidean spaces, represent a special class of fractional type vector-valued functions, which transform convex sets into convex sets. The aim of this paper is to show that a similar convexity preserving property holds within a new class of fractional type set-valued functions, acting between any real linear spaces.On continuous selections of finite-valued set-valued mappingshttps://www.zbmath.org/1463.540582021-07-26T21:45:41.944397Z"Zhukovskiĭ, Sergeĭ Evgen'evich"https://www.zbmath.org/authors/?q=ai:zhukovskiy.s-eSummary: Set-valued mappings with finite images are considered. For these mappings, a theorem on the existence of continuous selections is proved.Connectedness of the solution sets of inclusionshttps://www.zbmath.org/1463.540592021-07-26T21:45:41.944397Z"Zhukovskiy, E. S."https://www.zbmath.org/authors/?q=ai:zhukovskiy.evgeny-sThe author studies conditions for the connectedness of the solution set of the inclusion
\[
y_0 \in F(x),
\]
where \(F : D \multimap Y\) is a multimap of topological spaces, \(y_0 \in Y\). In particular, the following main result is proved.
Theorem. Suppose that \(D\) is a \(T_4\)-space and \(Y\) is a \(T_3\)-space and also: \((a)\) the set \(N = F^{-1}(y_0) \subset D\) is nonempty and closed; \((b)\) the set \(F(A)\) is closed in \(Y\) for each closed \(A \subset D\); \((c)\) for each \(x_0, x_1 \in N\) and an open neighborhood \(V\) of \(y_0\), there exists a closed subset \(N^\prime\) of \(D\) such that \(x_0, x_1 \in N^\prime\), and \(F(x) \cap V \neq \emptyset\) for all \(x \in N^\prime\). Then \(N\) is connected.
As application, the connectedness of the fixed point set of a Volterra (causal) multioperator \(G : D \subset C([0,a];\mathbb{R}^n) \multimap C([0,a];\mathbb{R}^n)\) with respect to the norm and weak topologies is considered. The second application deals with the connectedness of the solution set for a Volterra delay integral inclusion of Hammerstein type.New separation axioms in bitopological spaceshttps://www.zbmath.org/1463.540602021-07-26T21:45:41.944397Z"Abo-Elhamayel, M."https://www.zbmath.org/authors/?q=ai:abo-elhamayel.mohamed"Salleh, Zabidin"https://www.zbmath.org/authors/?q=ai:salleh.zabidinSummary: In this paper, new concepts of separation axioms are introduced in bitopological spaces. The implications of these new separation axioms among themselves as well as with other known separation axioms are obtained. Fundamental properties of the suggested concepts are also investigated. Furthermore, we introduced the concept of \(R_{ij}\)-neighborhoods and investigate some of their characterizations.Comments on some results related to soft separation axiomshttps://www.zbmath.org/1463.540612021-07-26T21:45:41.944397Z"Al-shami, T. M."https://www.zbmath.org/authors/?q=ai:al-shami.tareq-mohammad|al-shami.tareq-mohammedSummary: Separation axioms are among the most widespread, significant and motivating concepts via classical topology. They can be utilized to approach problems related to digital topology and to establish more restricted families of topological spaces. This matter applies to them via soft topology as well. Therefore many research studies about soft separation axioms and their properties have been carried out. However, we observe existing some errors over these studies which it can be attributed to the different types of belong and non-belong relations which were defined via the soft set theory, and to the chosen objects of study: are they ordinary points or soft points? Our desire of removing confusions and constructing accurate framework motivates us to do this investigation. Through this paper, we show some alleged findings obtained in [\textit{S. Bayramov} and \textit{C. G. Aras}, TWMS J. Pure Appl. Math. 9, No. 1, 82--93 (2018; Zbl 1430.54027); \textit{S. Hussain} and \textit{B. Ahmad}, Hacet. J. Math. Stat. 44, No. 3, 559--568 (2015; Zbl 1398.54017); \textit{M. Matejdes}, ``On soft regularity'', Int. J. Pure Appl. Math. 116, No. 1, 197--200 (2017; \url{doi:10.12732/ijpam.v116i1.21}); \textit{A. Singh} and \textit{N. Singh Noorie}, Ann. Fuzzy Math. Inform. 14, No. 5, 503--513 (2017; Zbl 1381.54005)] by giving convenient examples and then we formulate the right forms of these findings. In the last section, we demonstrate the relationships among soft \(T_4\)-spaces introduced in the previous studies and prove that all types of soft \(T_i\)-spaces are preserved under finitely soft product space in the cases of \(i=0, 1, 2\).Semiopen sets in ideal bitopological spaceshttps://www.zbmath.org/1463.540622021-07-26T21:45:41.944397Z"Caldas, M."https://www.zbmath.org/authors/?q=ai:caldas.m-j|caldas.michel|caldas.miguel"Jafari, S."https://www.zbmath.org/authors/?q=ai:jafari.sepehr|jafari.somaye|jafari.saeed|jafari.shahnaz|jafari.somayeh|jafari.samira|jafari.saeid.1|jafari.s-a-m|jafari.s-akbar|jafari.saeid.2|jafari.sajad|jafari.saeid|jafari.shahram|jafari.sayyed-heidar|jafari.shahla"Rajesh, N."https://www.zbmath.org/authors/?q=ai:rajesh.namegalesh|rajesh.n-r|rajesh.neelamegarajanSummary: The aim of this paper is to introduce and characterize the concepts of semiopen sets and their related notions in ideal bitopological spaces.Semi-separation axioms on invertible and semi-invertible spaceshttps://www.zbmath.org/1463.540632021-07-26T21:45:41.944397Z"Neethu, M."https://www.zbmath.org/authors/?q=ai:neethu.m"Jose, Anjaly"https://www.zbmath.org/authors/?q=ai:jose.anjalySummary: In this paper we introduce the concept of semi-invertibility with respect to a semi-open set. Here we examine some semi-separation axioms which are carried from subspaces to parent spaces with the help of invertibility and semi-invertibility. Also we study these properties on completely invertible and completely semi-invertible spaces.\(\mathcal{I}_{w\widehat{g}}\)-normal and \(\mathcal{I}_{w\widehat{g}}\)-regular spaceshttps://www.zbmath.org/1463.540642021-07-26T21:45:41.944397Z"Prabakaran, Thiruvalagu"https://www.zbmath.org/authors/?q=ai:prabakaran.thiruvalagu"Sangeethasubha, Vanangamudi"https://www.zbmath.org/authors/?q=ai:sangeethasubha.vanangamudi"Seenivasagan, Narayanasamy"https://www.zbmath.org/authors/?q=ai:seenivasagan.narayanasamy"Ravi, Ochadevar"https://www.zbmath.org/authors/?q=ai:ravi.ochadevarSummary: \(\mathcal{I}_{w\widehat{g}}\)-normal and \(\mathcal{I}_{w\widehat{g}}\)-regular spaces are introduced and various characterizations and properties are given. Characterizations of normal, mildly normal, \(w\widehat{g}\)-normal and regular spaces are also given.On \(\Lambda_g\)-normal and \(\Lambda_g\)-regular in ideal topological spaceshttps://www.zbmath.org/1463.540652021-07-26T21:45:41.944397Z"Rajasekaran, Ilangovan"https://www.zbmath.org/authors/?q=ai:rajasekaran.ilangovan"Nethaji, Ochanan"https://www.zbmath.org/authors/?q=ai:nethaji.ochananSummary: The aim of this paper, we introduce \(I_{\Lambda_g}\)-normal, \(_{\Lambda_g}I\)-normal and \(I_{\Lambda_g}\)-regular spaces using \(I_{\Lambda_g}\)-open sets and give characterizations and properties of such spaces. Also, characterizations of normal, mildly normal, \(\Lambda_g\)-normal and regular spaces are given.On selectively star-Lindelöf propertieshttps://www.zbmath.org/1463.540662021-07-26T21:45:41.944397Z"Bal, Prasenjit"https://www.zbmath.org/authors/?q=ai:bal.prasenjit"Bhowmik, Subrata"https://www.zbmath.org/authors/?q=ai:bhowmik.subrata"Gauld, David"https://www.zbmath.org/authors/?q=ai:gauld.david-bSummary: In this paper a new covering notion, called \(M\)-star-Lindelöf, is introduced and studied. This notion of covering arises from the selection hypothesis \(\mathsf{SS}^*_{\mathfrak D, fin}(\mathcal D, \mathfrak D)\). The stronger form \(\mathsf{SS}^*_{\mathfrak D, 1}(\mathcal D, \mathfrak D)\) of the selection hypothesis \(\mathsf{SS}^*_{\mathfrak D, fin}(\mathcal D, \mathfrak D)\) will also be discussed. We then consider weaker versions of these properties involving iterations of the star operator.Applications of limited information strategies in Menger's game.https://www.zbmath.org/1463.540672021-07-26T21:45:41.944397Z"Clontz, Steven"https://www.zbmath.org/authors/?q=ai:clontz.stevenRecall that a space \(X\) is said to have the Menger property if for each sequence \(\mathcal U_0,\mathcal U_1,\dots\) of open covers of \(X\) there are finite sets \(\mathcal V_0\subset\mathcal U_0,\mathcal V_1\subset\mathcal U_1,\dots\) such that \(\bigcup_{n<\omega}\mathcal V_n\) is a cover of \(X\). A naturally associated two-person game on \(X\), called the Menger game Men\((X)\), is defined as follows: players \(\mathcal C\) and \(\mathcal F\) play a round for each \(n<\omega\). In the round \(n\), \(\mathcal C\) chooses an open cover \(\mathcal U_n\) of \(X\), and \(\mathcal F\) responds by choosing a finite set \(F_n\subset X\) covered by a finite subfamily of \(\mathcal U_n\). \(\mathcal F\) wins the game if and only if \(\bigcup_{n<\omega}F_n=X\). It is a classical result by Hurewicz that a space \(X\) has the Menger property if and only if the player \(\mathcal C\) does not have a winning strategy in the game Men\((X)\).
The author investigates certain games related to the Menger game and defines classes of spaces using these games. In particular, the existence of a special winning strategy in Men\((X)\) for the player \(\mathcal F\) in the game Men\((X)\) is studied. Let \(k<\omega\) be an integer. A strategy \(\sigma\) for a player \(P\) is a \(k\)-Markov strategy for \(P\) if \(P\) considers the previous \(\le k\) moves of the opponent and the last move of the strategy owner before his next move. It is proved, among other interesting results, that: (1) a regular space \(X\) is \(\sigma\)-compact if and only if \(\mathcal F\) has a winning 1-Markov strategy in the game Men\((X)\); (2) if \(X\) is a second-countable space, then \(\mathcal F\) has a winning strategy in Men\((X)\) if and only if \(\mathcal F\) has a wining 1-Markov strategy in Men\((X)\); (3) \(\mathcal F\) has a winning 2-Markov strategy in the game Men\((L(\omega_1))\), but does not have a winning 1-Markov strategy in this game. Here \(L(\omega_1)\) is the one-point Lindelöfication of the discrete space \(\omega_1\).On star covering properties related to countable compactness and pseudocompactness.https://www.zbmath.org/1463.540682021-07-26T21:45:41.944397Z"Passos, Marcelo D."https://www.zbmath.org/authors/?q=ai:passos.marcelo-d"Santana, Heides L."https://www.zbmath.org/authors/?q=ai:santana.heides-l"da Silva, Samuel G."https://www.zbmath.org/authors/?q=ai:gomes-da-silva.samuelSummary: We prove a number of results on star covering properties which may be regarded as either generalizations or specializations of topological properties related to the ones mentioned in the title of the paper. For instance, we give a new, entirely combinatorial proof of the fact that \(\Psi\)-spaces constructed from infinite almost disjoint families are not star-compact. By going a little further we conclude that if \(X\) is a star-compact space within a certain class, then \(X\) is neither first countable nor separable. We also show that if a topological space is pseudonormal and has countable extent, then its Alexandroff duplicate satisfies property \((a)\). A number of problems and questions are also presented.A note on star Lindelöf, first countable and normal spaces.https://www.zbmath.org/1463.540692021-07-26T21:45:41.944397Z"Xuan, Wei-Feng"https://www.zbmath.org/authors/?q=ai:xuan.weifengUnder \(\mathsf{V}=\mathsf{L}\) it is shown that every star-Lindelöf, normal space with character at most \(\mathfrak{c}\) has countable extent. On the other hand it is shown that the tangent discs topology on the upper half-plane plus any subset \(A\) of the \(x\)-axis is star-Lindelöf and \(A\) is a closed discrete subspace: since it is already known that this space is first countable and is normal if \(A\) is a \(Q\)-set, and \(Q\)-sets exist under \(\mathsf{MA}+\neg\mathsf{CH}\) this illustrates that under this set-theoretic assumption there are spaces that are star-Lindelöf, normal and first countable but with uncountable extent.Spaces with property \((DC(\omega_1))\).https://www.zbmath.org/1463.540702021-07-26T21:45:41.944397Z"Xuan, Wei-Feng"https://www.zbmath.org/authors/?q=ai:xuan.weifeng"Shi, Wei-Xue"https://www.zbmath.org/authors/?q=ai:shi.wei-xueSummary: We prove that if \(X\) is a first countable space with property \((DC(\omega_1))\) and with a \(G_\delta\)-diagonal then the cardinality of \(X\) is at most \(\mathfrak{c}\). We also show that if \(X\) is a first countable, \(\mathrm{DCCC}\), normal space then the extent of \(X\) is at most \(\mathfrak{c}\).On star Lindelöf spaceshttps://www.zbmath.org/1463.540712021-07-26T21:45:41.944397Z"Xuan, Wei-Feng"https://www.zbmath.org/authors/?q=ai:xuan.weifeng"Song, Yan-Kui"https://www.zbmath.org/authors/?q=ai:song.yankuiA topological space \(X\) has cardinality at most \(2^{\mathfrak{c}}\) if it has a regular \(G_\delta\)-diagonal and \(X^2\) is star-Lindelöf or if there is a symmetric \(g\)-function such that \(\cap\{g^2(n,x)\mid n\in\omega\}=\{x\}\) and \(X\) is star Lindelöf. If a star Lindelöf Hausdorff space has Hausdorff pseudo-character \(\kappa\) then its extent is at most \(2^{2^\kappa}\). A Hausdorff space whose weak extent and Hausdorff pseudo-character are both \(\kappa\) has extent at most \(2^\kappa\).Notes on the general theorem of covering propertieshttps://www.zbmath.org/1463.540722021-07-26T21:45:41.944397Z"Zheng, Weipeng"https://www.zbmath.org/authors/?q=ai:zheng.weipengSummary: In this note, two general theorems about covering properties of topological spaces theory are established, which improve some previous theorems in literatures. Some counterexamples are constructed to negate some problems in literatures.More on \(P\)-closed spaceshttps://www.zbmath.org/1463.540732021-07-26T21:45:41.944397Z"Edwards, Terrence A."https://www.zbmath.org/authors/?q=ai:edwards.terrence-a"Joseph, James E."https://www.zbmath.org/authors/?q=ai:joseph.james-e"Nayar, Bhamini M. P."https://www.zbmath.org/authors/?q=ai:nayar.bhamini-m-pSummary: In [\textit{M. P. Berri} et al., in: General topology and its relations to modern analysis and algebra. Proceedings of the Kanpur Topological Conference, 1968. Prague: Academia. 93--114 (1971; Zbl 0235.54018)] the following problems were listed as open: Problem 14. Is a regular space in which every closed subset is regular-closed compact? Problem 15. Is a Urysohn-space in which every closed subset is Urysohn closed compact? To answer the question for Hausdorff-closed spaces in the affirmative, \textit{M. H. Stone} [Trans. Am. Math. Soc. 41, 375--481 (1937; JFM 63.1173.01)] used Boolean rings and \textit{M. Katětov} [Čas. Mat. Fys. 69, 36--49 (1940; JFM 66.0964.02)] used topological methods. In this article, all three questions are answered affirmatively using filters.On pseudocompactness and related notions in ZF.https://www.zbmath.org/1463.540742021-07-26T21:45:41.944397Z"Keremedis, Kyriakos"https://www.zbmath.org/authors/?q=ai:keremedis.kyriakosIt is well-known that some topological properties and implications/non-implications among them are closely related with certain set theories. Let ZF denote the Zermelo-Fraenkel set theory and let ZFC be the set theory ZF together with the axiom of choice AC. In this paper, the author studies in ZF and in the class of \(T_1\) spaces the web of implications and non-implications between the notions of pseudocompactness, light compactness, countable compactness and some of their ZFC or ZF+WFC equivalents, where WFC stands for some weak form of AC.Sequence compactness of covering topological space based on a subbasehttps://www.zbmath.org/1463.540752021-07-26T21:45:41.944397Z"Huang, Yichun"https://www.zbmath.org/authors/?q=ai:huang.yichun"Feng, Shukai"https://www.zbmath.org/authors/?q=ai:feng.shukai"Zhang, Xianyong"https://www.zbmath.org/authors/?q=ai:zhang.xianyongSummary: The covering topological space based on a subbase mainly introduces a covering (which constitutes a usual topological subbase) into the rough set framework to induce a variant topological space. At present, its topological properties concern only the connectedness, separability, countability and compactness. Thus, its sequence compactness is not previously studied but will be explored in this paper. Aiming at the covering topological space based on a subbase, the compactness is first deepened, the sequence compactness is then defined to achieve relevant properties, and an illustration example is finally provided. The obtained results systematically complete and deeply describe the covering topological space based on a subbase.Coproducts of proximity spaceshttps://www.zbmath.org/1463.540762021-07-26T21:45:41.944397Z"Grzegrzolka, Pawel"https://www.zbmath.org/authors/?q=ai:grzegrzolka.pawelSummary: In this paper, we introduce coproducts of proximity spaces. After exploring several of their basic properties, we show that given a collection of proximity spaces, the coproduct of their Smirnov compactifications proximally and densely embeds in the Smirnov compactification of the coproduct of the original proximity spaces. We also show that the dense proximity embedding is a proximity isomorphism if and only if the index set is finite. After constructing a number of examples of coproducts and their Smirnov compactifications, we explore several properties of the Smirnov compactification of the coproduct, including its metrizability, connectedness of the boundary, dimension, and its relation to the Stone-Čech compactification. In particular, we show that the Smirnov compactification of the infinite coproduct is never metrizable and that its boundary is highly disconnected. We also show that the proximity dimension of the Smirnov compactification of the coproduct equals the supremum of the covering dimensions of the individual Smirnov compactifications and that the Smirnov compactification of the coproduct is homeomorphic to the Stone-Čech compactification if and only if each individual proximity space is equipped with the Stone-Čech proximity. We finish with an example of a coproduct with the covering dimension 0 but the proximity dimension \(\infty\).Variations of uniform completeness related to realcompactness.https://www.zbmath.org/1463.540772021-07-26T21:45:41.944397Z"Hušek, Miroslav"https://www.zbmath.org/authors/?q=ai:husek.miroslavSeveral descriptions of (topological) realcompactness are transferred to uniform spaces. In this way non-equivalent concepts are obtained.
Their properties, relations and characterizations are discussed in the paper.
A Shirota-like characterization of a certain form of uniform realcompactness established by Garrido and Meroño for metrizable spaces is generalized to uniform spaces, cf. [\textit{M. I. Garrido} and \textit{A. S. Meroño}, Topology Appl. 241, 150--161 (2018; Zbl 1395.54022)].
The paper contains a lot of useful information. Indeed it yields a unifying interesting survey of known results to which numerous new observations have been added.About some properties of similarly homogeneous \(\mathbb{R} \)-treeshttps://www.zbmath.org/1463.540782021-07-26T21:45:41.944397Z"Bulygin, Alekseĭ Ivanovich"https://www.zbmath.org/authors/?q=ai:bulygin.aleksei-ivanovichSummary: In this paper we consider the properties of locally complete similarly homogeneous inhomogeneous \(\mathbb{R} \)-trees. The geodesic space is called \(\mathbb{R} \)-tree if any two points may be connected by the unique arc. The general problem of A. D. Alexandrov on the characterization of metric spaces is considered. The distance one preserving mappings are constructed for some classes of \(\mathbb{R} \)-trees. To do this, we use the construction with the help of which a new special metric is introduced on an arbitrary metric space. In terms of this new metric, a criterion is formulated that is necessary for a so that a distance one preserving mapping to be isometric. In this case, the characterization by A. D. Alexandrov is not fulfilled. Moreover, the boundary of a strictly vertical \(\mathbb{R} \)-tree is also studied. It is proved that any horosphere in a strictly vertical \(\mathbb{R} \)-tree is an ultrametric space. If the branch number of a strictly vertical \(\mathbb{R} \)-tree is not greater than the continuum, then the cardinality of any sphere and any horosphere in the \(\mathbb{R} \)-tree equals the continuum, and if the branch number of \(\mathbb{R} \)-tree is larger than the continuum, then the cardinality of any sphere or horosphere equals the number of branches.Some versions of second countability of metric spaces in ZF and their role to compactness.https://www.zbmath.org/1463.540792021-07-26T21:45:41.944397Z"Keremedis, Kyriakos"https://www.zbmath.org/authors/?q=ai:keremedis.kyriakosSummary: In the realm of metric spaces we show in ZF that:
(i) A metric space is compact if and only if it is countably compact and for every \(\varepsilon >0\), every cover by open balls of radius \(\varepsilon\) has a countable subcover.
(ii) Every second countable metric space has a countable base consisting of open balls if and only if the axiom of countable choice restricted to subsets of \(\mathbb{R}\) holds true.
(iii) A countably compact metric space is separable if and only if it is second countable.Continuous generalized metric spaceshttps://www.zbmath.org/1463.540802021-07-26T21:45:41.944397Z"Yu, Junche"https://www.zbmath.org/authors/?q=ai:yu.juncheSummary: Continuous generalized metric spaces are introduced and investigated in this paper. It is shown that for such spaces, \(c\)-Scott topology is equal to the generalized Scott topology, and that a non-expansive map between such spaces is Yoneda continuous if and only if it is continuous with respect to the generalized Scott topology.Completeness and cocompleteness of categories of Yoneda complete metric spacehttps://www.zbmath.org/1463.540812021-07-26T21:45:41.944397Z"Chen, Jinxin"https://www.zbmath.org/authors/?q=ai:chen.jinxinSummary: This paper investigates the completeness and cocompleteness of some categories of Yoneda complete metric space. It is shown that if the morphisms are chosen to be Yoneda continuous maps or Yoneda continuous nonexpansive maps, then the category is both complete and cocomplete. If the morphisms are chosen to be Yoneda continuous Lipschitz maps, then the category is finitely complete and finitely cocomplete, but neither complete nor cocomplete. It is also shown that the category of real-valued continuous lattice and Yoneda continuous right adjoints is complete.Huber's theorem and some results in bispaceshttps://www.zbmath.org/1463.540822021-07-26T21:45:41.944397Z"Mohanta, Sushanta Kumar"https://www.zbmath.org/authors/?q=ai:mohanta.sushanta-kumar"Patra, Shilpa"https://www.zbmath.org/authors/?q=ai:patra.shilpaSummary: In this paper, we obtain a generalized version of Huber's theorem in a suitable bispace and analyse some properties of the limit map of a sequence of continuous maps over such a bispace.Countable compactness of lexicographic products of GO-spaces.https://www.zbmath.org/1463.540832021-07-26T21:45:41.944397Z"Kemoto, Nobuyuki"https://www.zbmath.org/authors/?q=ai:kemoto.nobuyukiThe author presents a (rather technical) characterization of countable compactness in lexicographic products of GO-spaces (as defined in [\textit{N. Kemoto}, Topology Appl. 232, 267--280 (2017; Zbl 1382.54020)]). As in a GO-space any sequence has a monotone subsequence one need only worry about accumulation points for such sequences. Thus the characterization involves excluding unwanted appearances of closed sets of countable cofinality or coinitiality.
The paper concludes with many examples of products that are, or are not, countably compact. Since a (non-trivial) lexicographic product \(\prod_{n<\omega}X_n\) automatically has increasing and decreasing sequences the conditions are a bit more stringent on the factors starting from \(\omega\) and up. Thus, for example, \(\omega_1^\omega\) is countably compact but \(\omega_1^{\omega+1}\) is not.Property of being semi-Kelley for the cartesian products and hyperspaces.https://www.zbmath.org/1463.540842021-07-26T21:45:41.944397Z"Castañeda-Alvarado, Enrique"https://www.zbmath.org/authors/?q=ai:castaneda-alvarado.enrique"Vidal-Escobar, Ivon"https://www.zbmath.org/authors/?q=ai:vidal-escobar.ivonA continuum \(X\) is said to be \textit{Kelley} provided that for each point \(x\in X\), for each subcontinuum \(K\) of \(X\) containing \(x\) and for each sequence of points \(\{x_n\}\) of \(X\) converging to \(x\) there exists a sequence of subcontinua \(\{K_n\}\) of \(X\) such that for each \(n\in N\), \(x_n\in K_n\) and \(\lim K_n=K\). Let \(K\) be a subcontinuum of a continuum \(X\). A continuum \(M\subset K\) is called a \textit{maximal limit continuum in} \(K\) provided that there exists a sequence of subcontinua \(\{M_n\}\) of \(X\) converging to \(M\) such that for each convergent sequence of subcontinua \(\{M^{\prime}_{n}\}\) of \(X\) with \(M_n\subset M^{\prime}_{n}\) for each \(n\in N\) and \(\lim M^{\prime}_{n}=M^{\prime}\subset K\) we have that \(M^{\prime}=M\). A continuum \(X\) is said to be \textit{semi-Kelley} provided that for each subcontinuum \(K\) and for every two maximal limit continua \(M\) and \(L\) in \(K\) either \(M\subset L\) or \(L\subset M\).
In [Topol. Proc. 23(Spring), 69--99 (1998; Zbl 0943.54022)] \textit{J. J. Charatonik} and \textit{W. J. Charatonik} constructed a Kelley continuum \(X\) such that the cartesian product \(X\times X\) and the hyperspace \(2^X\) are not semi-Kelley. They also asked if it is true that if a continuum \(X\) is Kelley, then the cartesian product \(X\times[0,1]\) is semi-Kelley.
In the paper under review the authors construct a Kelley continuum \(X\) such that the cartesian product \(X\times[0,1]\) and the hyperspace \(C(X)\) are not semi-Kelley. Additionally, they show that small Whitney levels in \(C(X)\) are not semi-Kelley, answering a question posed by \textit{A. Illanes}.Edelstein type \(L\)-fuzzy fixed point theoremshttps://www.zbmath.org/1463.540852021-07-26T21:45:41.944397Z"Abdullahi, Muhammad Sirajo"https://www.zbmath.org/authors/?q=ai:abdullahi.muhammad-sirajo"Azam, Akbar"https://www.zbmath.org/authors/?q=ai:azam.akbar"Kumam, Poom"https://www.zbmath.org/authors/?q=ai:kumam.poomSummary: In this manuscript, we extend the idea of fuzzy fixed points to \(L\)-fuzzy fixed points and established some \(L\)-fuzzy fixed points results for \(L\)-fuzzy contractive and \(L\)-fuzzy locally contractive mappings on a compact metric space, our results extend some interesting results of the literature and some examples are also given to support the findings.A new approach to the study of fixed point for simulation functions with application in \(G\)-metric spaceshttps://www.zbmath.org/1463.540862021-07-26T21:45:41.944397Z"Afassinou, Komi"https://www.zbmath.org/authors/?q=ai:afassinou.komi"Narain, Ojen Kumar"https://www.zbmath.org/authors/?q=ai:narain.ojen-kumarSummary: The purpose of this work is to generalize the fixed point results of \textit{M. Kumar} and \textit{R. Sharma} [Bol. Soc. Parana. Mat. (3) 37, No. 2, 115--121 (2019; Zbl 1413.54134)] by introducing the concept of \(( \alpha,\beta )\)-\(\mathcal{Z}\)-contraction mapping, Suzuki generalized \(( \alpha,\beta )\)-\(\mathcal{Z}\)-contraction mapping, \(( \alpha,\beta )\)-admissible mapping and triangular \(( \alpha,\beta )\)-admissible mapping in the framework of \(G\)-metric spaces. Fixed point theorems for these classes of mappings are established in the framework of complete \(G\)-metric spaces and we establish a generalization of the fixed point result of [loc. cit.] and a host of others in the literature. Finally, we apply our fixed point result to solve an integral equation.A common fixed point result for two pairs of weakly tangential maps in B-metric spaceshttps://www.zbmath.org/1463.540872021-07-26T21:45:41.944397Z"Akkouchi, Mohamed"https://www.zbmath.org/authors/?q=ai:akkouchi.mohamedSummary: In a previous paper, [\textit{M. Akkouchi}, Commun. Math. Anal. 11, No. 1, 111--120 (2011; Zbl 1206.54034)], the so called property (W.T) was introduced. By this property, it is aimed a common generalization of several concepts, like the concept of noncompatible mappings due to Jungck, the property (E.A) of Aamri and Moutawakil and the concept of asymptotically regular maps due to Browder and Petryshyn. The purpose of this paper is to use that property (W.T) to prove a general common fixed point result for two pairs of weakly compatible maps under a contractive condition of Lipschitz type in the setting of b-metric spaces. The well-posedness of the fixed point problem for these maps is also investigated. Our main result involves a Lipschitz type condition which is is not a contractive condition of the classical type. An example applying our result is furnished.An extension of Tychonoff fixed point theorem with application to the solvability of the infinite systems of integral equations in the Fréchet spaceshttps://www.zbmath.org/1463.540882021-07-26T21:45:41.944397Z"Allahyari, Reza"https://www.zbmath.org/authors/?q=ai:allahyari.reza"Arab, Reza"https://www.zbmath.org/authors/?q=ai:arab.reza"Haghighi, Ali Shole"https://www.zbmath.org/authors/?q=ai:shole-haghighi.aliSummary: In the present article, we introduce a new concept of contraction and prove a new type of the extension of Tychonoff fixed point theorem. Then, as an application, we study the problem of existence of solutions for the infinite systems of integral equations using the technique of measures of noncompactness in conjunction with this extension in the Fréchet spaces.Nonunique fixed point theorems on \(b\)-metric spaces via simulation functionshttps://www.zbmath.org/1463.540892021-07-26T21:45:41.944397Z"Aydi, Hassen"https://www.zbmath.org/authors/?q=ai:aydi.hassen"Karapinar, Erdal"https://www.zbmath.org/authors/?q=ai:karapinar.erdal"Rakočević, Vladimir"https://www.zbmath.org/authors/?q=ai:rakocevic.vladimirSummary: Based on the concepts of \(\alpha\)-orbital admissibility given by \textit{O.~Popescu} in [Fixed Point Theory Appl. 2014, Paper No.~190, 12~p. (2014; Zbl 1451.54020)] and simulation functions introduced by \textit{F.~Khojasteh} et al. in [Filomat 29, No.~6, 1189--1194 (2015; Zbl 1462.54072)], we introduce in this paper different types of contractive mappings. We also provide some nonunique fixed point results for such contractive mappings in the class of orbital complete \(b\)-metric spaces. Some known results are shown follow from ours.Some Prešić type results in \(b\)-dislocated metric spaceshttps://www.zbmath.org/1463.540902021-07-26T21:45:41.944397Z"Babu, A. Som"https://www.zbmath.org/authors/?q=ai:babu.a-som"Dosenovic, Tatjana"https://www.zbmath.org/authors/?q=ai:dosenovic.tatjana"Ali, Md. Mustaq"https://www.zbmath.org/authors/?q=ai:ali.md-mustaq"Radenovic, Stojan"https://www.zbmath.org/authors/?q=ai:radenovic.stojan"Rao, K. P. R."https://www.zbmath.org/authors/?q=ai:rao.koduru-pandu-rangaSummary: In this paper, we obtain a Prešić type common fixed point theorem for four maps in \(b\)-dislocated metric spaces. We also present one example to illustrate our main theorem. Further, we obtain two more corollaries.Some fixed point theorems of Hardy-Roger contraction in complex valued \(b\)-metric spaceshttps://www.zbmath.org/1463.540912021-07-26T21:45:41.944397Z"Chantakun, Warinsinee"https://www.zbmath.org/authors/?q=ai:chantakun.warinsinee"Prasert, Jaruwan"https://www.zbmath.org/authors/?q=ai:prasert.jaruwanSummary: The aim of this paper is to prove the existence and uniqueness of a fixed point of a mapping satisfying the Hardy-Rogers contraction in complex-valued \(b\)-metric space, we have obtained some fixed point theorems in complex-valued \(b\)-metric spaces. This work is generalized and improved some results of \textit{D. Hasanah} [``Fixed point theorem in complex-valued \(b\)-metric space'', Cauchy: Jurnal Matematika Murni dan Aplikasi 4, No. 4, 138--145 (2017; \url{doi:10.18860/ca.v4i4.3669})], and well-known results in the literature.Common fixed point theorems for Geraghty's type contraction mapping with two generalized metrics endowed with a directed graph in JS-metric spaceshttps://www.zbmath.org/1463.540922021-07-26T21:45:41.944397Z"Charoensawan, Phakdi"https://www.zbmath.org/authors/?q=ai:charoensawan.phakdiSummary: The purpose of this work is to present some existence results for common fixed point theorems for Geraghty contraction mappings with two generalized metrics endowed with a directed graph in JS-metric spaces. Some examples supporting our main results are also presented.Endpoints for contractive multi-valued maps on the metric space of partially ordered module with monotonic lawshttps://www.zbmath.org/1463.540932021-07-26T21:45:41.944397Z"Cheng, Congdian"https://www.zbmath.org/authors/?q=ai:cheng.congdian"Xu, Xiaoxiao"https://www.zbmath.org/authors/?q=ai:xu.xiaoxiao"Guan, Hongyan"https://www.zbmath.org/authors/?q=ai:guan.hongyanSummary: In this paper we develop the metric space of partially ordered module with monotonic laws and the related convergence of sequences, which extend the cone metric space and the related convergence of sequences introduced in 2007. We establish three endpoint theorems for contractive multi-valued maps on such space, which cover some recent results of the fixed point theory. Our contributions not only extend the range and the depth of the fixed point research area, but also advance the mutual influences between analysis and algebra.On contractions via simulation functions on extended \(b\)-metric spaceshttps://www.zbmath.org/1463.540942021-07-26T21:45:41.944397Z"Chifu, Cristian"https://www.zbmath.org/authors/?q=ai:chifu.cristian"Karapınar, Erdal"https://www.zbmath.org/authors/?q=ai:karapinar.erdalSummary: In this paper, we introduce the notion of an admissible extended \(\mathcal{Z}\)-contraction mapping in the setting of extended \(b\)-metric spaces. As an application, we consider Ulam stability problems based on our contractions. The presented results cover several existing results in the literature.Some fixed point results for \(\mathcal{JHR}\) operator pairs in \(C^*\)-algebra valued modular \(b\)-metric spaces via \(C_*\) class functions with applicationshttps://www.zbmath.org/1463.540952021-07-26T21:45:41.944397Z"Das, Dipankar"https://www.zbmath.org/authors/?q=ai:das.dipankar"Mishra, Lakshmi Narayan"https://www.zbmath.org/authors/?q=ai:mishra.lakshmi-narayanSummary: In this paper, we introduce \(C^*\)-algebra valued modular \(b\)-metric spaces. Some common fixed point theorem for \(\mathcal{JHR}\) operator pairs with new contractive conditions via \(C_*\)-class functions in \(C^*\)-algebra valued modular \(b\)-metric spaces is given here with examples. Some applications to nonlinear integral equations and operator equations are also presented.$G$-approximate fixed point theorems and the $G$-orthogonality in $G$-metric spaceshttps://www.zbmath.org/1463.540962021-07-26T21:45:41.944397Z"Dehghan Nezhad, A."https://www.zbmath.org/authors/?q=ai:dehghan-nezhad.a"Mazaheri, H."https://www.zbmath.org/authors/?q=ai:mazaheri.hamidSummary: In this contribution we define $G$-orthogonality and $G$-approximation fixed point and investigated some results on them. We also prove some $G$-approximate fixed point theorems without using the condition that the $G$-metric space \(X\) is complete.Intuitionistic fuzzy \(\psi\)-\(\phi\)-contractive mappings and fixed point theorems in non-Archimedean intuitionistic fuzzy metric spaceshttps://www.zbmath.org/1463.540972021-07-26T21:45:41.944397Z"Dinda, Bivas"https://www.zbmath.org/authors/?q=ai:dinda.bivas"Samanta, T. K."https://www.zbmath.org/authors/?q=ai:samanta.tapas-kumar|samanta.tapas-kr"Jebril, Iqbal H."https://www.zbmath.org/authors/?q=ai:jebril.iqbal-hamzhSummary: In this paper, intuitionistic fuzzy Banach contraction theorem for $M$-complete non-Archimedean intuitionistic fuzzy metric spaces and intuitionistic fuzzy Edelstein contraction theorem for non-Archimedean intuitionistic fuzzy metric spaces by intuitionistic fuzzy \(\psi\)-\(\phi\) contractive mappings are proved.Tripled coincidence point theorems for mixed \(g\)-\(R\)-monotone operators in metric spaces endowed with a reflexive relationhttps://www.zbmath.org/1463.540982021-07-26T21:45:41.944397Z"Dobrican, Melánia-Iulia"https://www.zbmath.org/authors/?q=ai:dobrican.melania-iuliaSummary: In this paper we present some results regarding tripled coincidence points of mixed \(g\)-\(R\)-monotone operators in the framework of metric spaces endowed with a reflexive relation. Our results extend and generalize some famous results obtained by Berinde, Borcut, Ćirić and Lakshmikantham.Suzuki type fixed point result for rational \(\theta \)-contraction on complete metric spaceshttps://www.zbmath.org/1463.540992021-07-26T21:45:41.944397Z"Durmaz, G."https://www.zbmath.org/authors/?q=ai:durmaz.gonca"Minak, G."https://www.zbmath.org/authors/?q=ai:minak.gulhan"Altun, I."https://www.zbmath.org/authors/?q=ai:altun.ishakSummary: In this paper, we present a new approach to fixed point theorems for single valued contraction mappings defined on complete metric spaces. We introduce a new concept called Suzuki type rational \({\theta^*}\)-contraction and prove fixed point result for such mappings. Also, we give some examples showing that our result is a real generalization of some existing results.Revisiting of some outstanding metric fixed point theorems via $E$-contractionhttps://www.zbmath.org/1463.541002021-07-26T21:45:41.944397Z"Fulga, Andreea"https://www.zbmath.org/authors/?q=ai:fulga.andreea"Karapınar, Erdal"https://www.zbmath.org/authors/?q=ai:karapinar.erdalSummary: In this paper, we introduce the notion of $\alpha$-$\phi$-contractive mapping of type $E$, to remedy of the weakness of the existing contraction mappings. We investigate the existence and uniqueness of a fixed point of such mappings. We also list some examples to illustrate our results that unify and generalize the several well-known results including the famous Banach contraction mapping principle.\(C\)-class functions on common fixed point theorems for weak contraction mapping of integral type in modular spaceshttps://www.zbmath.org/1463.541012021-07-26T21:45:41.944397Z"Hammad, H. A."https://www.zbmath.org/authors/?q=ai:hammad.hasanen-abuelmagd"Rashwan, R. A."https://www.zbmath.org/authors/?q=ai:rashwan.rashwan-ahmed"Ansari, A. H."https://www.zbmath.org/authors/?q=ai:ansari.abul-hasan|ansari.arslan-hojet|ansari.athar-hussain|ansari.arslan-hojt|ansari.arslan-hojat|ansari.arsalan-hojat|ansari.arsalan-hojjat|ansari.a-halim|ansari.arslan-hojjatSummary: In this paper, we use the concept of \(C\)-class functions introduced by the third author [``\(\varphi\)-\(\psi\)-contractive type mappings and related fixed point'', in: Proceedings of the 2nd regional conference on mathematics and applications, Payame Noor University, Tehran. 377--380 (2014)] to prove the existence and uniqueness of a common fixed point for self-mappings in modular spaces of integral inequality. Our results extended and generalized previous known results in this direction.Some new types multivalued \(F\)-contractions on quasi metric spaces and their fixed pointshttps://www.zbmath.org/1463.541022021-07-26T21:45:41.944397Z"Hançer, Hatice Aslan"https://www.zbmath.org/authors/?q=ai:hancer.hatice-aslan"Olgun, Murat"https://www.zbmath.org/authors/?q=ai:olgun.murat"Altun, Ishak"https://www.zbmath.org/authors/?q=ai:altun.ishakSummary: In this paper we present two new results for the existence of fixed points of multivalued mappings with closed values on quasi metric space. First we introduce the multivalued \(F_d\)-contraction on quasi metric space \((X,d)\) and give a fixed point result related to this concept. Then taking into account the \(Q\)-function on a quasi metric space, we establish a \(Q\)-function version of this concept as multivalued \(F_q\)-contraction and hence we present a fixed point result to see the effect of \(Q\)-function to existence of fixed point of multivalued mappings on quasimetric space.Fixed point theorems under \(c\)-distance in ordered cone metric spaces over Banach algebrashttps://www.zbmath.org/1463.541032021-07-26T21:45:41.944397Z"Han, Yan"https://www.zbmath.org/authors/?q=ai:han.yan"Xu, Shaoyuan"https://www.zbmath.org/authors/?q=ai:xu.shaoyuan"Duan, Jiangmei"https://www.zbmath.org/authors/?q=ai:duan.jiangmei"Zhang, Jianyuan"https://www.zbmath.org/authors/?q=ai:zhang.jianyuanSummary: In this paper, some fixed point theorems under \(c\)-distance in ordered cone metric spaces over Banach algebras are obtained. The results improve and generalize some well-known comparable results. Some supporting examples are also given.On the common coincidence theorem of three mappingshttps://www.zbmath.org/1463.541042021-07-26T21:45:41.944397Z"Hao, Yan"https://www.zbmath.org/authors/?q=ai:hao.yan"Guan, Hongyan"https://www.zbmath.org/authors/?q=ai:guan.hongyanSummary: In order to obtain the condition under which three mappings have common coincidence points, a new \(\phi\)-contraction condition of three mappings \(A, B, S\) from a topological space \(X\) to a complete \(b\)-metric space \(Y\) is first introduced. Under a set of specific conditions, starting from any point in \(X\), a special point sequence in \(Y\) is constructed by a specific iterative algorithm. By using the new \(\phi\)-contraction condition of three mappings, the upper semi-continuity of a multivariate function \(\phi\), the monotonic increase of each variable and the lemma, we prove that the point sequence is a Cauchy sequence in \(Y\), so it is convergent. Secondly, by using the proper mapping conditions of \(A, B, S\) and the closeness of image, combined with the new \(\phi\)-contraction condition, it is proved that under the given different conditions, the three mappings have common coincidence points by reduction to absurdity. Finally, according to the conclusion, a concrete example is constructed to illustrate the application of the theory.Common fixed point theorems of several mappings in S-metric spaceshttps://www.zbmath.org/1463.541052021-07-26T21:45:41.944397Z"Huang, Qi"https://www.zbmath.org/authors/?q=ai:huang.qi"Xue, Xifeng"https://www.zbmath.org/authors/?q=ai:xue.xifengSummary: Firstly, the definitions of metric spaces, compatibility and some properties in S-metric spaces are given. Then we study the existence and uniqueness of common fixed points under the contraction conditions of several compatible mappings in S-metric spaces.Fixed point theorems in \(G\)-cone metric spaceshttps://www.zbmath.org/1463.541062021-07-26T21:45:41.944397Z"Huang, Qi"https://www.zbmath.org/authors/?q=ai:huang.qi"Xue, Xifeng"https://www.zbmath.org/authors/?q=ai:xue.xifengSummary: In this paper, we obtain both fixed point theorems under the contraction condition of self-mapping and common fixed point theorems under the contraction condition of weak compatible self-mappings by introducing weak compatible mapping into \(G\)-cone metric spaces. Furthermore, we prove them by the iterative method.Some random coincidence point and common fixed point results in cone metric spaces over Banach algebrashttps://www.zbmath.org/1463.541072021-07-26T21:45:41.944397Z"Jiang, Binghua"https://www.zbmath.org/authors/?q=ai:jiang.binghua"Cai, Zelin"https://www.zbmath.org/authors/?q=ai:cai.zelin"Chen, Jinyang"https://www.zbmath.org/authors/?q=ai:chen.jinyangSummary: In this paper, we obtain some tripled common random fixed point and tripled random fixed point theorems with several generalized Lipschitz constants in cone metric spaces. We consider the obtained assertions without the assumption of normality of cones. The presented results generalize some coupled common fixed point theorems in the existing literature.A type new \(\alpha\)-admissible mappings and related common fixed point theoremshttps://www.zbmath.org/1463.541082021-07-26T21:45:41.944397Z"Jiang, Binghua"https://www.zbmath.org/authors/?q=ai:jiang.binghua"Cai, Zelin"https://www.zbmath.org/authors/?q=ai:cai.zelin"Li, Biwen"https://www.zbmath.org/authors/?q=ai:li.biwen"Chen, Jinyang"https://www.zbmath.org/authors/?q=ai:chen.jinyangSummary: In this paper, we introduce the triangular \(\alpha\)-admissible mapping in the setting of cone metric spaces equipped with Banach algebra and solid cones. In terms of the normal conditions of the cone, our results generalize and extend several known common fixed point theorems of metric and cone metric spaces.Notes on some recent papers concerning \(F\)-contractions in \(b\)-metric spaceshttps://www.zbmath.org/1463.541092021-07-26T21:45:41.944397Z"Kadelburg, Zoran"https://www.zbmath.org/authors/?q=ai:kadelburg.zoran"Radenović, Stojan"https://www.zbmath.org/authors/?q=ai:radenovic.stojanSummary: In several recent papers, attempts have been made to apply Wardowski's method of \(F\)-contractions in order to obtain fixed point results for single and multivalued mappings in \(b\)-metric spaces. In this article, it is shown that in most cases the conditions imposed on respective mappings are too strong and that the results can be obtained directly, i.e., without using most of the properties of auxiliary function \(F\).Best proximity point theorems for \(G\)-proximal weak contractions in complete metric spaces endowed with graphshttps://www.zbmath.org/1463.541102021-07-26T21:45:41.944397Z"Klanarong, Chalongchai"https://www.zbmath.org/authors/?q=ai:klanarong.chalongchai"Suantai, Suthep"https://www.zbmath.org/authors/?q=ai:suantai.suthepSummary: In this paper, the existence of best proximity point theorems for two new types of nonlinear non-self mappings in a complete metric space endowed with a directed graph are established. Our main results extend and generalize many known results in the literatures. As a special case of the main results, best proximity point theorems on partially ordered sets are obtained.Some generalizations of weak cyclic compatible contractionshttps://www.zbmath.org/1463.541112021-07-26T21:45:41.944397Z"Kumari, P. Sumati"https://www.zbmath.org/authors/?q=ai:kumari.panda-sumati"Nantadilok, Jamnian"https://www.zbmath.org/authors/?q=ai:nantadilok.jamnian"Sarwar, Muhammad"https://www.zbmath.org/authors/?q=ai:sarwar.muhammadSummary: In this paper, we establish the existence theorems for weak cyclic compatible contractions and cyclic compatible \(M_k\)-contractions. Our results extend and improve existing known results in [the first author and \textit{D. Panthi}, Fixed Point Theory Appl. 2015, Paper No. 153, 17 p. (2015; Zbl 06584101)] as well as other results in the literature. We provide examples to illustrate and support our main results.Common fixed point theorem for Ćirić type quasi-contractions in rectangular \(b\)-metric spaceshttps://www.zbmath.org/1463.541122021-07-26T21:45:41.944397Z"Li, Shu-Fang"https://www.zbmath.org/authors/?q=ai:li.shufang"He, Fei"https://www.zbmath.org/authors/?q=ai:he.fei"Lu, Ning"https://www.zbmath.org/authors/?q=ai:lu.ningSummary: The purpose of this paper is to give positive answers to questions concerning Ćirić type quasi-contractions in rectangular \(b\)-metric spaces proposed in [\textit{R. George} et al., J. Nonlinear Sci. Appl. 8, No. 6, 1005--1013 (2015; Zbl 1398.54068)].Some fixed point theorems in complete \(v\)-generalized metric spaceshttps://www.zbmath.org/1463.541132021-07-26T21:45:41.944397Z"Liu, Xianpeng"https://www.zbmath.org/authors/?q=ai:liu.xianpeng"Ji, Peisheng"https://www.zbmath.org/authors/?q=ai:ji.peishengSummary: The contractive mapping of \(C\)-class function in the setting of metric space is generalized in this paper. The iterative method in complete \(v\)-generalized metric space is used to prove the fixed point theorem of the \(C\)-class function on \( (\psi, \phi)\)-type contractive mapping. We also prove the fixed point theorems of the generalized \(F\)-type contractive mapping and generalized \(\theta\)-type contractive mapping.Some fixed point theorems in logarithmic convex structures.https://www.zbmath.org/1463.541142021-07-26T21:45:41.944397Z"Moazzen, Alireza"https://www.zbmath.org/authors/?q=ai:moazzen.alireza"Cho, Yoel-Je"https://www.zbmath.org/authors/?q=ai:cho.yoel-je"Park, Choonkil"https://www.zbmath.org/authors/?q=ai:park.choonkil"Eshaghi Gordji, Madjid"https://www.zbmath.org/authors/?q=ai:eshaghi-gordji.madjidSummary: In this paper, we introduce the concept of a logarithmic convex structure. Let \(X\) be a set and \(D:X\times X\rightarrow [1,\infty)\) a function satisfying the following conditions:\par \ \ (i) For all \(x,y\in X\), \(D(x,y)\geq 1\) and \(D(x,y)=1\) if and only if \(x=y\).\par \ (ii) For all \(x,y\in X\), \(D(x,y)=D(y,x)\).\par (iii) For all \(x,y,z\in X\), \(D(x,y)\leq D(x,z)D(z,y)\).\par (iv) For all \(x,y,z\in X\), \(z\neq x,y\) and \(\lambda\in(0,1)\), \[D(z,W(x,y,\lambda))\leq D^\lambda(x,z)D^{1-\lambda}(y,z),\] \[D(x,y)=D(x,W(x,y,\lambda))D(y,W(x,y,\lambda)),\] where \(W:X\times X\times[0,1]\rightarrow X\) is a continuous mapping. We name this the logarithmic convex structure. In this work we prove some fixed point theorems in the logarithmic convex structure.Common fixed point theorems for a class of integral Altman type mapping with applicationshttps://www.zbmath.org/1463.541152021-07-26T21:45:41.944397Z"Nie, Hui"https://www.zbmath.org/authors/?q=ai:nie.hui"Zhang, Shuyi"https://www.zbmath.org/authors/?q=ai:zhang.shuyiSummary: The purpose of this paper is to study the existence of fixed point theorems for a new class of integral Altman type mappings. By using the compatible conditions of self-mapping pair in non-Archimedean Menger probabilistic metric spaces, common fixed point theorems for integral Altman type mapping are established in non-Archimedean Menger probabilistic metric spaces. Furthermore, the existence and uniqueness of solutions are also discussed for a class of systems of functional equations arising in dynamic programming, which improve and extend some known results.Fixed points of weakly compatible mappings in fuzzy metric spaceshttps://www.zbmath.org/1463.541162021-07-26T21:45:41.944397Z"Pant, Badri Datt"https://www.zbmath.org/authors/?q=ai:pant.badridatt-d"Chauhan, Sunny"https://www.zbmath.org/authors/?q=ai:chauhan.sunny"Cho, Yeol Je"https://www.zbmath.org/authors/?q=ai:cho.yeol-je"Eshaghi-Gordji, Madjid"https://www.zbmath.org/authors/?q=ai:eshaghi-gordji.madjidSummary: In this paper, we prove some common fixed point theorems for weakly compatible mappings in fuzzy metric spaces with common property (E.A) and give some examples to illustrate our results. As an application to our main result, we present a common fixed point theorem for four finite families of self mappings in fuzzy metric spaces by using the notion of the pairwise commuting mappings. Our results improve and extend some relevant results existing in the literature.Common fixed points for two mappings with implicit-linear contractions on partially ordered 2-metric spaceshttps://www.zbmath.org/1463.541172021-07-26T21:45:41.944397Z"Piao, Yongjie"https://www.zbmath.org/authors/?q=ai:piao.yongjieSummary: In this paper, we introduce a new class \(U\) of 3-dimensional real functions, use \(U\) and a 2-dimensional real function \(\phi \) to construct a new implicit-linear contractive condition, obtain some existence theorems of common fixed points for two mappings on partially ordered 2-metric spaces, and give a sufficient condition under which there exists a unique common fixed point. The obtained results generalize and improve the corresponding conclusions in references.Absorbing mappings and fixed points in \(G\)-metric spaceshttps://www.zbmath.org/1463.541182021-07-26T21:45:41.944397Z"Popa, Valeriu"https://www.zbmath.org/authors/?q=ai:popa.valeriu"Patriciu, Alina-Mihaela"https://www.zbmath.org/authors/?q=ai:patriciu.alina-mihaelaSummary: In this paper a general fixed point theorem for two pairs of absorbing mappings satisfying a new type of common limit range property in \(G\)-metric spaces is proved.FG-coupled fixed point theorems for various contractions in partially ordered metric spaceshttps://www.zbmath.org/1463.541192021-07-26T21:45:41.944397Z"Prajisha, E."https://www.zbmath.org/authors/?q=ai:prajisha.e"Shaini, P."https://www.zbmath.org/authors/?q=ai:shaini.pSummary: In this paper we introduce FG-coupled fixed point, which is a generalization of coupled fixed point for nonlinear mappings in partially ordered complete metric spaces. We discuss existence and uniqueness theorems of FG-coupled fixed points for different contractive mappings. Our theorems generalize the results of \textit{T. G. Bhaskar} and \textit{V. Lakshmikantham} [Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 65, No. 7, 1379--1393 (2006; Zbl 1106.47047)].Unique common fixed point theorem for four maps in complex valued \(S\)-metric spaceshttps://www.zbmath.org/1463.541202021-07-26T21:45:41.944397Z"Rao, K. P. R."https://www.zbmath.org/authors/?q=ai:rao.koduru-pandu-ranga"Ali, M. Mustaq"https://www.zbmath.org/authors/?q=ai:ali.md-mustaqSummary: In this paper we obtain a common fixed point theorem for the two weakly compatible pairs of mappings satisfying a contractive condition in complex valued \(S\)-metric spaces.A common fixed point theorem for four maps satisfying generalized \(\alpha\)-weakly contractive condition in ordered partial metric spaceshttps://www.zbmath.org/1463.541212021-07-26T21:45:41.944397Z"Rao, K. P. R."https://www.zbmath.org/authors/?q=ai:rao.koduru-pandu-ranga"Sombabu, A."https://www.zbmath.org/authors/?q=ai:sombabu.aSummary: In this paper we obtain a common fixed point theorem for four maps satisfying generalized \(\alpha\)-weakly contractive condition and we give an example to illustrate our main theorem. Our result generalize and improve the theorem of \textit{S. Cho} [Fixed Point Theory Appl. 2018, Paper No. 3, 18 p. (2018; Zbl 1462.54047)].Topological degree theory in fuzzy metric spaces.https://www.zbmath.org/1463.541222021-07-26T21:45:41.944397Z"Rashid, M. H. M."https://www.zbmath.org/authors/?q=ai:rashid.malik-h-m|rashid.mohammad-hussein-mohammadSummary: The aim of this paper is to modify the theory to fuzzy metric spaces, a natural extension of probabilistic ones. More precisely, the modification concerns fuzzily normed linear spaces, and, after defining a fuzzy concept of completeness, fuzzy Banach spaces. After discussing some properties of mappings with compact images, we define the (Leray-Schauder) degree by a sort of colimit extension of (already assumed) finite dimensional ones. Then, several properties of thus defined concept are proved. As an application, a fixed point theorem in the given context is presented.Some multi-valued contraction theorems on \(\mathcal{H} \)-cone metrichttps://www.zbmath.org/1463.541232021-07-26T21:45:41.944397Z"Rehman, Saif Ur"https://www.zbmath.org/authors/?q=ai:ur-rehman.saif"Jabeenb, Shamoona"https://www.zbmath.org/authors/?q=ai:jabeenb.shamoona"Muhammad"https://www.zbmath.org/authors/?q=ai:muhammad.naseer|muhammad.m-rashith|muhammad.shafiq|muhammad.rebin-a|muhammad.khurram|muhammad.kamran|muhammad.azam-sheikh|muhammad.ibrahim-dauda|muhammad.nazeer|muhammad.khan|muhammad.ashraf|muhammad.adnan|muhammad.shahabuddin|muhammad.abubakr|muhammad.suleman|muhammad.shoaib-arif|muhammad.aslam|muhammad.jan|muhammad.ammar-k|muhammad.lawal|muhammad.raees-ul-haq|muhammad.tanveer|muhammad.noryanti|muhammad.lutta|muhammad.tauqeer|muhammad.mehwish-hussain|muhammad.mayinur|muhammad.yousaf-shad|muhammad.ali|muhammad.arshad|muhammad.faqir|muhammad.taseer|muhammad.shakoor|muhammad.muhathir|muhammad.iqbal|muhammad.shah|muhammad.wazir|muhammad.khairun-nisak|muhammad.ayyaz|muhammad.ghulam|muhammad.ahmed|muhammad.nasim|muhammad.s-s"Ullah, Hayat"https://www.zbmath.org/authors/?q=ai:ullah.hayat"Hanifullah"https://www.zbmath.org/authors/?q=ai:hanifullah.Summary: In this paper we define some new type of multi-valued contraction maps on \(\mathcal{H} \)-cone metric and proved some fixed point and common fixed point theorems in the setting of cone metric spaces.Some fixed point results in partial S-metric spaceshttps://www.zbmath.org/1463.541242021-07-26T21:45:41.944397Z"Rezaee, M. M."https://www.zbmath.org/authors/?q=ai:rezaee.mohammad-mahdi"Sedghi, S."https://www.zbmath.org/authors/?q=ai:sedghi.shaban"Mukheimer, A."https://www.zbmath.org/authors/?q=ai:mukheimer.aiman-a-s|mukheimer.aimen-a-s"Abodayeh, K."https://www.zbmath.org/authors/?q=ai:abodayeh.k-h|abodayeh.kamal|abodayeh.kamaleldin"Mitrović, Z. D."https://www.zbmath.org/authors/?q=ai:mitrovic.zoran-dSummary: We introduce in this article a new class of generalized metric spaces, called partial S-metric spaces. In addition, we also give some interesting results on fixed points in the partial S-metric spaces and some applications.Common fixed point theorems for two pairs of self-mappings in complex-valued metric spaceshttps://www.zbmath.org/1463.541252021-07-26T21:45:41.944397Z"Rouzkard, Fayyaz"https://www.zbmath.org/authors/?q=ai:rouzkard.fayyazSummary: In this paper, we consider complex-valued metric space and prove some coincidence point and common fixed point theorems involving two pairs of self-mappings satisfying the contraction condition with complex coefficients in these spaces. In this paper, we generalize, improve and simplify the proofs of some existing results.Cyclic representations and fixed pointshttps://www.zbmath.org/1463.541262021-07-26T21:45:41.944397Z"Rus, Ioan A."https://www.zbmath.org/authors/?q=ai:rus.ioan-aSummary: The present paper discusses an aspect of the open Problem 17 in [\textit{I. A. Rus} et al., Fixed point theory 1950--2000. Romanian contributions. Cluj-Napoca: House of the Book of Science (2002; Zbl 1005.54037)] (p. 148): Let \((X, d)\) be a complete metric space and \(Y\subset X\times X\). An operator \(f: X\to X\) is an \((Y, a)\)-contraction if \(a\in[0, 1[\) and
\[
d(f(x), f(y))\leq ad(x, y)\quad\text{for all }(x,y)\in Y.
\]
The problem is to construct a fixed point theory for \((Y, a)\)-contractions, or more generally for \((Y, a)\)-generalized contractions.Coincidence point theorems for cyclic multi-valued and hybrid contractive mappingshttps://www.zbmath.org/1463.541272021-07-26T21:45:41.944397Z"Saksirikun, Warut"https://www.zbmath.org/authors/?q=ai:saksirikun.warut"Berinde, Vasile"https://www.zbmath.org/authors/?q=ai:berinde.vasile"Petrot, Narin"https://www.zbmath.org/authors/?q=ai:petrot.narinSummary: In this paper, we consider the existence theorem of coincidence point for a pair of single-valued and multi-valued mapping that are concerned with the concepts of cyclic contraction type mapping. Some illustrative examples and remarks are also discussed.\((F,\varphi,\alpha)_s\)-contractions in \(b\)-metric spaces and applicationshttps://www.zbmath.org/1463.541282021-07-26T21:45:41.944397Z"Sangurlu Sezen, M."https://www.zbmath.org/authors/?q=ai:sangurlu-sezen.mSummary: In this paper, we introduce more general contractions called \(\varphi\)-fixed point point for \((F,\varphi,\alpha)_s\) and \((F,\varphi,\alpha)_s\)-weak contractions. We prove the existence and uniqueness of \(\varphi\)-fixed point point for \((F,\varphi,\alpha)_s\) and \((F,\varphi,\alpha)_s\)-weak contractions in complete \(b\)-metric spaces. Some examples are supplied to support the usability of our results. As applications, necessary conditions to ensure the existence of a unique solution for a nonlinear inequality problem are also discussed. Also, some new fixed point results in partial metric spaces are proved.Some common fixed point results in 2-Banach spaceshttps://www.zbmath.org/1463.541292021-07-26T21:45:41.944397Z"Sarkar, Krishnadhan"https://www.zbmath.org/authors/?q=ai:sarkar.krishnadhan"Barman, Dinanath"https://www.zbmath.org/authors/?q=ai:barman.dinanath"Tiwary, Kalishankar"https://www.zbmath.org/authors/?q=ai:tiwary.kalishankarSummary: In this paper, we have proved some common fixed point theorems of a family of self maps without continuity in 2-Banach space. We have used functions on \(R_+{}^5\) to \(R_+\) and also generalize many existing results.On fixed points of contraction maps acting in \((q_1, q_2)\)-quasimetric spaces and geometric properties of these spaceshttps://www.zbmath.org/1463.541302021-07-26T21:45:41.944397Z"Sengupta, Richik"https://www.zbmath.org/authors/?q=ai:sengupta.richikSummary: We study geometric properties of \((q_1, q_2)\)-quasimetric spaces and fixed point theorems in these spaces. In paper [\textit{A. V. Arutyunov} and \textit{A. V. Greshnov}, Dokl. Math. 94, No. 1, 434--437 (2016; Zbl 1352.54030); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 469, No. 5, 527--531 (2016)], a fixed point theorem was obtained for a contraction map acting in a complete \((q_1, q_2)\)-quasimetric space. The graph of the map was assumed to be closed. In this paper, we show that this assumption is essential, i.e. we provide an example of a complete quasimetric space and a contraction map acting in it whose graph is not closed and which is fixed-point-free. We also describe some geometric properties of such spaces.Common fixed point theorem in Menger space using \((CLRg)\) propertyhttps://www.zbmath.org/1463.541312021-07-26T21:45:41.944397Z"Sharma, Varsha"https://www.zbmath.org/authors/?q=ai:sharma.varshaSummary: The object of this paper is to establish a common fixed point theorem for semi-compatible pair of self maps by using \(CLRg\) property in menger space.Modified Banach fixed point results for locally contractive mappings in complete \(G_d\)-metric like spacehttps://www.zbmath.org/1463.541322021-07-26T21:45:41.944397Z"Shoaib, Abdullah"https://www.zbmath.org/authors/?q=ai:shoaib.abdullah"Nisar, Zubair"https://www.zbmath.org/authors/?q=ai:nisar.zubair"Hussain, Aftab"https://www.zbmath.org/authors/?q=ai:hussain.aftab"Özer, Özen"https://www.zbmath.org/authors/?q=ai:ozer.ozen"Arshad, Muhammad"https://www.zbmath.org/authors/?q=ai:arshad.muhammad-sarmad|arshad.muhammad-junaidSummary: In this paper we discuss unique fixed point of mappings satisfying a locally contractive condition on a closed ball in a complete \(G_d\)-metric like space. Examples have been given to show the novelty of our work. Our results improve/generalize several well-known recent and classical results.On dislocated quasi metric spaces satisfying certain rational inequalitieshttps://www.zbmath.org/1463.541332021-07-26T21:45:41.944397Z"Shukla, Krati"https://www.zbmath.org/authors/?q=ai:shukla.kratiSummary: We consider the dislocated quasi metric spaces satisfying certain rational inequalities. We establish some new results related to fixed points. In order to illustrate the existence of the fixed points, we construct some examples in this paper.A fixed point theorem for cyclic-contractive mapping of Pata typehttps://www.zbmath.org/1463.541342021-07-26T21:45:41.944397Z"Sima, Aolei"https://www.zbmath.org/authors/?q=ai:sima.aolei"He, Fei"https://www.zbmath.org/authors/?q=ai:he.fei"Lu, Ning"https://www.zbmath.org/authors/?q=ai:lu.ningSummary: In this paper, the cyclic form of Pata type fixed point theorems is discussed by using the modular arithmetic method. In metric spaces, we establish a fixed point theorem for cyclic-contractive mapping of Pata type. The results obtained in this paper improve and unify the main results of some existing literatures.Fixed point theorems for several cyclic-contractive mappings in dislocated quasi-\(b\)-metric spaceshttps://www.zbmath.org/1463.541352021-07-26T21:45:41.944397Z"Sima, Aolei"https://www.zbmath.org/authors/?q=ai:sima.aolei"He, Fei"https://www.zbmath.org/authors/?q=ai:he.fei"Lu, Ning"https://www.zbmath.org/authors/?q=ai:lu.ningSummary: Fixed point theorems for several cyclic contractive mappings are established in dislocated quasi-\(b\)-metric spaces. The results obtained in this paper improve and unify some previous results in the existing literature. Moreover, several nontrivial examples are given to illustrate the superiority of the main results.\(S\)-metric and fixed point theoremhttps://www.zbmath.org/1463.541362021-07-26T21:45:41.944397Z"Simkhah Asil, M."https://www.zbmath.org/authors/?q=ai:asil.m-simkhah"Sedghi, Sh."https://www.zbmath.org/authors/?q=ai:sedghi.shahram|sedghi.shaban"Shobe, N."https://www.zbmath.org/authors/?q=ai:shobe.nabi"Mitrović, Z. D."https://www.zbmath.org/authors/?q=ai:mitrovic.zoran-dSummary: In this paper, we prove a general fixed point theorem in \(S\)-metric spaces for maps satisfying an implicit relation on complete metric spaces. As applications, we get many analogues of fixed point theorems in metric spaces for \(S\)-metric spaces.Some remarks on the paper ``Fixed point of \(\alpha\)-Geraghty contraction with applications''https://www.zbmath.org/1463.541372021-07-26T21:45:41.944397Z"Singh, K. Anthony"https://www.zbmath.org/authors/?q=ai:singh.k-anthonySummary: \textit{M. Arshad} et al. [Sci. Bull., Ser. A, Appl. Math. Phys., Politeh. Univ. Buchar. 78, No. 2, 67--78 (2016; Zbl 1413.54100)] improved the notion of \(\alpha\)-Geraghty contraction type mappings and established some common fixed point theorems for a pair of \(\alpha\)-admissible mappings under the improved notion of \(\alpha\)-Geraghty contraction type condition in a complete metric space. But we observe some gaps in the proof of some theorems in the paper due to some insufficiency in the defining condition of the associated contraction mappings. The aim of this paper is to attempt to bridge the gaps by proposing some modifications in the contraction condition of the mappings.Remarks on the paper: ``\(\alpha$-$\psi\)-Geraghty contraction type mappings and some related fixed point results''https://www.zbmath.org/1463.541382021-07-26T21:45:41.944397Z"Singh, K. Anthony"https://www.zbmath.org/authors/?q=ai:singh.k-anthonySummary: Recently, \textit{E.~Karapinar} [Filomat 28, No.~1, 37--48 (2014; Zbl 1450.54017)] introduced the notion of generalized \(\alpha$-$\psi\)-Geraghty contraction type mappings in the setting of a metric space and proved the existence and uniqueness of a fixed point of such mappings. But we observe that the condition (H1) for the uniqueness of the fixed point of such mappings as proposed by Karapinar is not enough. The aim of this paper is to attempt to rectify it by proposing a slightly stronger condition in place of condition~(H1).Fixed point theorems for generalized rational \(\alpha\)-\(\psi\)-Geraghty contraction type mappings in metric spacehttps://www.zbmath.org/1463.541392021-07-26T21:45:41.944397Z"Singh, K. Anthony"https://www.zbmath.org/authors/?q=ai:singh.k-anthony"Singh, M. R."https://www.zbmath.org/authors/?q=ai:singh.medini-r|singh.mahi-r|singh.manas-ranjan|singh.maibam-ranjit"Singh, Th. Chhatrajit"https://www.zbmath.org/authors/?q=ai:chhatrajit-singh.th|singh.thokchom-chhatrajitSummary: In this paper, we introduce the notion of generalized rational \(\alpha\)-\(\psi\)-Geraghty contraction type mappings in the context of metric space and establish some fixed point theorems for such mappings. An example is also given to illustrate our result.Coupled coincidence points for \(F\)-contractive type mappings in partially ordered metric spaceshttps://www.zbmath.org/1463.541402021-07-26T21:45:41.944397Z"Song, Jiping"https://www.zbmath.org/authors/?q=ai:song.jipingSummary: In this article, some coupled coincidence point results for two mappings \(g: X \to X\) and \(G: X \times X \to X\) satisfying \(F\)-contractive type conditions are obtained, and some coupled fixed point results are derived in partially ordered metric spaces. A sufficient condition for uniqueness of a coupled point of coincidence is established for \(F\) type contractions, and a coupled common fixed point theorem is obtained. Some examples are given to support our results.Coupled coincidence and coupled common fixed point theorems on a fuzzy metric space with a graphhttps://www.zbmath.org/1463.541412021-07-26T21:45:41.944397Z"Sumalai, Phumin"https://www.zbmath.org/authors/?q=ai:sumalai.phumin"Kumam, Poom"https://www.zbmath.org/authors/?q=ai:kumam.poom"Gopal, Dhananjay"https://www.zbmath.org/authors/?q=ai:gopal.dhananjaySummary: Inspired by the work of \textit{D. Eshi} et al. [Fixed Point Theory Appl. 2016, Paper No. 37, 14 p. (2016; Zbl 1336.54042)], we introduce a new class of \(G\)-\(f\)-contraction mappings in complete fuzzy metric spaces endowed with a directed graph and prove some existence results for coupled coincidence and coupled common fixed point theorems of this type of contraction mappings in complete fuzzy metric spaces endowed with a directed graph.A new common fixed point theorem for \(R\)-weakly commuting mappings in the \(S\)-metric spacehttps://www.zbmath.org/1463.541422021-07-26T21:45:41.944397Z"Sun, Yuxin"https://www.zbmath.org/authors/?q=ai:sun.yuxin"Gu, Feng"https://www.zbmath.org/authors/?q=ai:gu.feng.1|gu.fengSummary: In \(S\)-metric space, using the \(R\)-weakly commuting condition of self-image pairs, a new common fixed point theorem for two kinds of mappings under \(R\)-weakly commuting conditions is established in a complete \(S\)-metric space. The results further develop and improve the relevant results of the existing literature.Some new fixed point theorems for pairs of sub-compatible maps in \({D^*}\)-metric spaceshttps://www.zbmath.org/1463.541432021-07-26T21:45:41.944397Z"Tao, Tao"https://www.zbmath.org/authors/?q=ai:tao.tao"Xue, Xifeng"https://www.zbmath.org/authors/?q=ai:xue.xifengSummary: For complete \({D^*}\)-metric spaces, the notions of mapping pair sub-compatibility are firstly put forward. Then the existence and uniqueness of common fixed point for four self-mappings are discussed. Some new fixed point theorems are proved, which improved several relative results largely.Cone \({\mathrm{D}^*}\)-metric spaces over Banach algebras and common fixed point theoremshttps://www.zbmath.org/1463.541442021-07-26T21:45:41.944397Z"Tao, Tao"https://www.zbmath.org/authors/?q=ai:tao.tao"Xue, Xifeng"https://www.zbmath.org/authors/?q=ai:xue.xifengSummary: Based on the concept of complete cone \({\mathrm{D}^*}\)-metric spaces over Banach algebras, the notions of some new contractive mappings are firstly put forward. Then the existence and uniqueness of common fixed point for two continuous self-mappings are discussed. Some new fixed point theorems are proved, which improved several relative results in literatures.Fixed point results of generalized almost \(G\)-contractions in metric spaces endowed with graphshttps://www.zbmath.org/1463.541452021-07-26T21:45:41.944397Z"Tiammee, Jukrapong"https://www.zbmath.org/authors/?q=ai:tiammee.jukrapongSummary: The main aim of this paper is to introduce a class of generalized contractions in the sense of Berinde. Some examples and fixed point theorems for such mappings in the setting of metric spaces endowed with a graph are discussed. Our results extend and include many existing results in the literature.Some fixed point results for Caristi type mappings in modular metric spaces with an applicationhttps://www.zbmath.org/1463.541462021-07-26T21:45:41.944397Z"Turkoglu, Duran"https://www.zbmath.org/authors/?q=ai:turkoglu.duran"Kilinç, Emine"https://www.zbmath.org/authors/?q=ai:kilinc.emineSummary: In this paper we give Caristi type fixed point theorem in complete modular metric spaces. Moreover we give a theorem which can be derived from Caristi type. Also an application for the bounded solution of functional equations is investigated.Common fixed point theorem for generalized Suzuki type \( (\psi, \varphi)\)-weakly contractive mappingshttps://www.zbmath.org/1463.541472021-07-26T21:45:41.944397Z"Zhang, Jie"https://www.zbmath.org/authors/?q=ai:zhang.jie.1|zhang.jie.5|zhang.jie.3|zhang.jie|zhang.jie.4|zhang.jie.2"Suyalatu"https://www.zbmath.org/authors/?q=ai:suyalatu.Summary: In pertinent literature, the Suzuki type common fixed point theorem in complete metric space has been established. Based on this theorem, the Suzuki type common fixed point theorem for two mappings in a complete \(b\)-metric space is established.Common fixed point theorems for a class of integral type contractive mappings in fuzzy metric spaceshttps://www.zbmath.org/1463.541482021-07-26T21:45:41.944397Z"Zhang, Shuyi"https://www.zbmath.org/authors/?q=ai:zhang.shuyi"Zhang, Xinyu"https://www.zbmath.org/authors/?q=ai:zhang.xinyu"Nie, Hui"https://www.zbmath.org/authors/?q=ai:nie.huiSummary: The existence of a common fixed point for a class of integral type contractive mappings in complete fuzzy metric spaces is studied. Several new common fixed point theorems for this class of integral type contractive mappings in complete fuzzy metric spaces are established under certain conditions. An example is also given to illustrate the validity of the result, which improves and extends the corresponding results of some references.Common fixed point theorems for a class of integral type set-valued mapping sequenceshttps://www.zbmath.org/1463.541492021-07-26T21:45:41.944397Z"Zhang, Xinyu"https://www.zbmath.org/authors/?q=ai:zhang.xinyu"Zhang, Shuyi"https://www.zbmath.org/authors/?q=ai:zhang.shuyi"Zheng, Xiaodi"https://www.zbmath.org/authors/?q=ai:zheng.xiaodiSummary: The purpose of this paper is to study the existence of common fixed points for a class of integral type set-valued mapping sequences in non-Archimedes probabilistic 2-metric spaces. By using the correlation lemmas, we establish some common fixed point theorems for a class of integral type set-valued mapping sequences in non-Archimedes probabilistic 2-metric spaces, which improves and extends some related corresponding results.Some properties of multivalued functions in digital topologyhttps://www.zbmath.org/1463.541502021-07-26T21:45:41.944397Z"Cinar, Ismet"https://www.zbmath.org/authors/?q=ai:cinar.ismet"Karaca, Ismet"https://www.zbmath.org/authors/?q=ai:karaca.ismetSummary: In this paper, we define the approximate fixed point property between digital multivalued functions. We also give the definition of universal digital multivalued functions. We introduce some properties of the smash product of digital multivalued functions. Finally, we give some results on morphological operators.Category of H-groupshttps://www.zbmath.org/1463.550022021-07-26T21:45:41.944397Z"Pakdaman, Ali"https://www.zbmath.org/authors/?q=ai:pakdaman.ali"Torabi, Hamid"https://www.zbmath.org/authors/?q=ai:torabi.hamid"Mashayekhy, Behrooz"https://www.zbmath.org/authors/?q=ai:mashayekhy.behroozSummary: This paper develops a basic theory of H-groups. We introduce a special quotient of H-groups and extend some algebraic constructions of topological groups to the category of H-groups and H-maps and then present a functor from this category to the category of quasitopological groups.Metric space of subcopulashttps://www.zbmath.org/1463.600162021-07-26T21:45:41.944397Z"Rachasingho, Jumpol"https://www.zbmath.org/authors/?q=ai:rachasingho.jumpol"Tasena, Santi"https://www.zbmath.org/authors/?q=ai:tasena.santiSummary: Sklar's theorem states that any joint distribution function can be written as a composition of its marginal distributions and a subcopula. Structural study of the latter is therefore natural. In this work, we define a new metric on the space of subcopulas making the space of copula its subspace. This is done via suitably extended subcopulas to joint distribution functions. Relationship between this new metric and the previously defined metric on the space of subcopulas is also discussed.Weaknesses analysis of C string functions based on topological spacehttps://www.zbmath.org/1463.680142021-07-26T21:45:41.944397Z"Gong, Mengxiao"https://www.zbmath.org/authors/?q=ai:gong.mengxiao"Xie, Huiyang"https://www.zbmath.org/authors/?q=ai:xie.huiyangSummary: There are many weaknesses of C language without checking boundaries. It is an innovative method to analyze the weaknesses based on point-set topology. In this paper, the continuity of topological space is used to solve the problem of string functions. It is proved that the character set stored in the string array is a topological space on the given subset family according to the definition of point-set topology. The string function could be a continuous mapping while there is not any weakness. So there are some weaknesses to be solved if it could not guarantee a continuous mapping. The continuity of topological space can be used to determine whether the code is right or not. It can promote the code writing and lead to write a better programming language.On a duality between time and space coneshttps://www.zbmath.org/1463.830022021-07-26T21:45:41.944397Z"Al-Qallaf, Waleed"https://www.zbmath.org/authors/?q=ai:al-qallaf.waleed"Papadopoulos, Kyriakos"https://www.zbmath.org/authors/?q=ai:papadopoulos.kyriakosSummary: We give an exact mathematical construction of a spacelike order \(<\), which is dual to the standard chronological order \(\ll\) in the \(n\)-dimensional Minkowski space \(M^n\), and we discuss its order-theoretic, geometrical as well as its topological implications, conjecturing a possible extension to curved spacetimes.