Recent zbMATH articles in MSC 40Chttps://www.zbmath.org/atom/cc/40C2021-04-16T16:22:00+00:00WerkzeugGeneralized limits and sequence of matrices.https://www.zbmath.org/1456.400102021-04-16T16:22:00+00:00"Özgüç, İ."https://www.zbmath.org/authors/?q=ai:ozguc.ilknur"Taş, E."https://www.zbmath.org/authors/?q=ai:tas.emre"Yurdakadim, T."https://www.zbmath.org/authors/?q=ai:yurdakadim.tugbaLet \(\mathcal{B}=(B_i)_{i\in \mathbb{N}}\) be a sequence of infinite matrices with non-negative entries which defines a regular summability method. Denote by \(m\) the space of all bounded real-valued sequences equipped with the supremum norm.
The authors introduce and study two types of linear functionals on \(m\) which enjoy certain properties, called \(S_{\mathcal{B}}\)-limits and \(\mathcal{B}\)-Banach limits.
For instance, it is proved that the set \(SL_{\mathcal{B}}\) of \(S_{\mathcal{B}}\)-limits and the set \(BL_{\mathcal{B}}\) of \(\mathcal{B}\)-Banach limits have a non-empty intersection and that \(BL_{\mathcal{B}}\) coincides with the set of ordinary Banach limits
if and only if \(\mathcal{B}\) is strongly regular.
Reviewer: Jan-David Hardtke (Leipzig)A new type of difference class of interval numbers.https://www.zbmath.org/1456.460032021-04-16T16:22:00+00:00"Baruah, Achyutananda"https://www.zbmath.org/authors/?q=ai:baruah.achyutananda"Dutta, Amar Jyoti"https://www.zbmath.org/authors/?q=ai:dutta.amar-jyotiSummary: In this article we introduce the notation difference operator \(\Delta_m\) (\(m \geq 0\) be an integer) for studying some properties defined with interval numbers. We introduced the classes of sequence \(\bar{\ell}(p)(\Delta_m)\), \(\bar{c}(p)(\Delta_m)\) and \(\bar{c}_0(\Delta_m)\) and investigate different algebraic properties like completeness, solidness, convergence free etc.Approximation by sub-matrix means of multiple Fourier series in the Hölder metric.https://www.zbmath.org/1456.420102021-04-16T16:22:00+00:00"Krasniqi, Xhevat Z."https://www.zbmath.org/authors/?q=ai:krasniqi.xhevat-zahir|krasniqi.xhevat-zSummary: In this paper some results on approximation by sub-matrix means of multiple Fourier series in the Hölder metric are obtained. Our results are applicable for a wider class of sequences and give a better degree of approximation than those presented previously by others.Almost everywhere strong \(C,1,0\) summability of 2-dimensional trigonometric Fourier series.https://www.zbmath.org/1456.420112021-04-16T16:22:00+00:00"Goginava, Ushangi"https://www.zbmath.org/authors/?q=ai:goginava.ushangiSummary: In this paper we study the a. e. exponential strong \((C, 1, 0)\) summability of of the 2-dimensional trigonometric Fourier series of the functions belonging to \(L (\log^+L)^2\).Some new triple sequence spaces over \(n\)-normed space.https://www.zbmath.org/1456.460072021-04-16T16:22:00+00:00"Jalal, Tanweer"https://www.zbmath.org/authors/?q=ai:jalal.tanweer"Malik, Ishfaq Ahmad"https://www.zbmath.org/authors/?q=ai:malik.ishfaq-ahmadSummary: Triple sequence spaces were introduced by \textit{A. Şahiner} et al. [Selçuk J. Appl. Math. 8, No. 2, 49--55 (2007; Zbl 1152.40306)]. The main objective of this paper is to define some new classes of triple sequences over $n$-normed space by means of Musielak-Orlicz function and difference operators. We also study some algebraic and topological properties of these new sequence spaces.On some double sequence spaces of interval number.https://www.zbmath.org/1456.460062021-04-16T16:22:00+00:00"Gölbol, Sibel Yasemin"https://www.zbmath.org/authors/?q=ai:golbol.sibel-yasemin"Esi, Ayhan"https://www.zbmath.org/authors/?q=ai:esi.ayhan"Değer, Uğur"https://www.zbmath.org/authors/?q=ai:deger.ugurSummary: \textit{A. Esi} and \textit{S. Yasemin} [``Some spaces of sequences of interval numbers defined by a modulus function'', Global J. Math. Anal. 2, No. 1, 11--16 (2014; \url{doi:10.14419/gjma.v2i1.2005})] defined the metric spaces \(\overline{c}_0(f,p,s)\), \(\overline{c}(f,p,s)\), \(\overline{l}_\infty (f,p,s)\) and \(\overline{l}_p(f,p,s)\) of sequences of interval numbers by a modulus function. In this study, we consider a generalization for double sequences of these metric spaces by taking a \(\psi\) function, satisfying the following conditions, instead of \(s\) parameter. For this aim, let \(\psi(k, l)\) be a positive function for all \(k, l \in \mathbb{N}\) such that
\begin{itemize}
\item[(i)] \(\underset{k,l\rightarrow\infty}{\lim} \psi(k,l)=0,\)
\item[(ii)] \(\Delta_2 \psi(k,l) = \psi(k-1,l-1) -2\psi(k,l) + \psi(k+1,l+1) \geq 0\)
\end{itemize}
or
\(\psi(k,l)=1\).
Therefore, according to class of functions which satisfying the conditions (i) and (ii) we deal with the metric spaces \(\overline{c}_0^2(f,p,\psi)\), \(\overline{c}^2(f,p,\psi)\), \(\overline{l}_\infty^2(f,p,\psi)\) and \(\overline{l}_p^2(f,p,\psi)\) of double sequences of interval numbers defined by a modulus function.Infinite matrices and some matrix transformations.https://www.zbmath.org/1456.400072021-04-16T16:22:00+00:00"Eren, Rahmet Savaş"https://www.zbmath.org/authors/?q=ai:eren.rahmet-savasSummary: The goal of this paper is to define the spaces $V_{\sigma_ 0}^\lambda (p)$ and $V_{\sigma}^\lambda (p) $ by using de la Vallée Poussin and invariant mean. Furthermore we
characterize certain matrices in $V_\sigma^\lambda$ which will fill a gap in the existing
literature.