×

A weak contractive condition and some fixed point theorems. (English) Zbl 1444.54030

Castillo, Oscar (ed.) et al., Recent advances in intelligent information systems and applied mathematics. Selected papers based on the presentations at the 2nd international conference on information technology and applied mathematics, ICITAM 2019, Haldia Institute of Technology, Haldia, India, March 7–9, 2019. Cham: Springer. Stud. Comput. Intell. 863, 822-834 (2020).
Summary: Fixed point theorems for weak-\(\left( \psi ,\alpha ,\beta \right) \)-contractive mappings have been introduced and investigated for different kinds of metric spaces. The paper first discusses a particular condition and then a weak contractive condition generalizing existing such conditions is defined. Our primary aim is to investigate the Banach, Kannan and Chatterjea’s fixed point theorems in complete metric spaces satisfying the new weak contractive condition and their applications. In the sequel, several auxiliary results are investigated and also incorporated sufficient number of examples in suitable places to justify certain claims.
For the entire collection see [Zbl 1436.68020].

MSC:

54H25 Fixed-point and coincidence theorems (topological aspects)
47H10 Fixed-point theorems
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Banach, S.: Sur les operations dans les ensembles abstraits et leur application aux equations integerales. Fund. Math. 3, 133-181 (1922) · JFM 48.0201.01 · doi:10.4064/fm-3-1-133-181
[2] Kannan, R.: Some results on fixed points. Bull. Calcutta Math. Soc. 60, 71-76 (1968) · Zbl 0209.27104
[3] Chatterjea, S.K.: Fixed point theorems. C.R. Acad. Bulgare Sci. 25, 727-730 (1972) · Zbl 0274.54033
[4] Dorić, D.: Common fixed point for generalized \(\left( \psi,\phi \right)-\) weak contractions. Appl. Math. Lett. 22, 1896-1900 (2009) · Zbl 1203.54040 · doi:10.1016/j.aml.2009.08.001
[5] Moradi, S., Davood, A.: New extension of Kannan fixed point theorem on complete metric and generalized metric spaces. Int. J. Math. Anal. 5, 2313-2320 (2011) · Zbl 1296.54075
[6] Eslamian, M., Abkar, A.: A fixed point theorem for generalized weakly contractive mappings in complete metric space. Italian J. Pure Appl. Math. (in press) · Zbl 1277.47069
[7] Cherichi, M., Samet, B.: Fixed point theorems on ordered gauge spaces with applications to nonlinear integral equations. Fixed Point Theory Appl. 13, 1-19 (2012) · Zbl 1273.54048
[8] Razani, A., Parvaneh, V.: Some fixed point theorems for weakly \(T\)-Chatterjea and weakly \(T\)-Kannan-contractive mappings in complete metric spaces. Russ. Math. (Izv. VUZ.) 57, 38-45 (2013) · Zbl 1270.54052
[9] Kir, M., Kiziltunc, H.: The concept of weak \(\left( \psi,\alpha,\beta \right)\) for some well known fixed point theorems. J. Ana. Num. Theor. 3, 137-142 (2015) · doi:10.18576/jant/030210
[10] Kir, M., Kiziltunc, H.: The concept of weak \(\left( \psi,\alpha,\beta \right)\) contractions in partially ordered metric spaces. J. Nonlinear Sci. Appl. 8, 1141-1149 (2015) · Zbl 1331.54056 · doi:10.22436/jnsa.008.06.23
[11] Choudhury, B.S., Kundu, A.: \( \left( \psi,\alpha,\beta \right)-\) weak contractions in partially ordered metric spaces. Appl. Math. Lett. 25, 6-10 (2012) · Zbl 1269.54021 · doi:10.1016/j.aml.2011.06.028
[12] Işık, H., Türkoğlu, D.: Common fixed points for \(\left( \psi,\alpha,\beta \right)-\) weakly contractive mappings in generalized metric spaces. Fixed Point Theory Appl. 2013, 133 (2013) · Zbl 1429.54058 · doi:10.1186/1687-1812-2013-133
[13] Kir, M., Kiziltunc, H.: Weakly \(T_F-\) type contractive mappings. Int. J. Pure Appl. Math. 101, 43-53 (2015) · doi:10.12732/ijpam.v101i1.5
[14] Fadail, Z.M., Ahmad, A.G.B., Ansari, A.H., Radenovic, S., Rajovi, M.: Some common fixed point results of mappings in \(0-\sigma -\) complete metric-like spaces via new function. Appl. Math. Sci. 9(83), 4109-4127 (2015)
[15] Babu, G.V.R., Sailaja, P.D.: A fixed point theorem of generalized weakly contractive maps in orbitally complete metric spaces. Thai J. Math. 9, 1-10 (2011) · Zbl 1259.54017
[16] Bilgili, N., Karapınar, E., Turkoglu, D.: A note on common fixed points for \(\left( \psi,\alpha,\beta \right)-\) weak contractive mappings in generalized metric spaces. Fixed Point Theory Appl. 2013, 287 (2013) · Zbl 1469.54065 · doi:10.1186/1687-1812-2013-287
[17] Geraghty, M.: On contractive mappings. Proc. Amer. Math. Soc. 40, 604-608 (1973) · Zbl 0245.54027 · doi:10.1090/S0002-9939-1973-0334176-5
[18] Branciari, A.: A fixed point theorem for mapping satisfying a general contractive condition of integral type. Int. J. Math. Math. Sci. 29, 531-536 (2002) · Zbl 0993.54040 · doi:10.1155/S0161171202007524
[19] Moradi, S., Beiranvand, A.: Fixed point of \(T_F\)-contractive single-valued mappings. Iran. J. Math. Sci. Inform. 5, 25-32 (2010) · Zbl 1301.46029
[20] Kadelburg, Z., Paunović, L., Radenović, S.: A note on fixed point theorems for weakly \(T-\) Kannan and weakly \(T-\) Chatterjea contractions in \(b-\) metric spaces. Gulf J. Math. 3, 57-67 (2015) · Zbl 1389.54093
[21] Filipović, M., Paunović, L.R., Radenović, S., Rajović, M.: Remarks on cone metric spaces and fixed point theorems of \(T\)-Kannan contractive mappings. Math. Comput. Model. 54, 1467-1472 (2011) · Zbl 1228.54039 · doi:10.1016/j.mcm.2011.04.018
[22] Radenović,
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.