Some results on multi-valued weakly Jungck mappings in \(b\)-metric space
type: Item
instance of: scholarly article
title: Some results on multi-valued weakly Jungck mappings in \(b\)-metric space
zbMATH Open document ID: 1175.47055
published in: Central European Journal of Mathematics
publication date: 2009-01-05T00:00:00Z
review text: Let \((X, d)\) be a \(b\)-metric space, \(S, T : X \to CB(X)\). The pair \((S, T)\) is called a multivalued \((\theta,\varphi)\)-weak \(J\)-contraction if there exists a constant \(\theta \in (0, 1)\) and a continuous monotone increasing function \(\varphi : \mathbb{R}^+ \to \mathbb{R}^+\) satisfying \(\varphi(0) = 0\), such that \(H(Tx, Ty) \leq \theta d(Sx, Sy) + \varphi(D(Sy, Tx))\), for all \(x, y \in X\). (This definition is a generalization of the corresponding definition in \textit{M.\,Berinde} and \textit{V.\,Berinde} [J.~Math.\ Anal.\ Appl.\ 326, No.\,2, 772--782 (2007; Zbl 1117.47039)]. Under the additional hypotheses that \(T(X) \subset S(X)\), with \(S(X)\) a complete subspace of \(CB(X)\), and \(S\) is continuous, the author proves that \(S\) and \(T\) have a common coincidence point \(z\) and obtains an error estimate for \(d(Sx_n, Sz)\). The second theorem in the paper is a similar result using a different contractive condition.
Mathematics Subject Classification ID: 47H10
Mathematics Subject Classification ID: 54H25
Mathematics Subject Classification ID: 47H08
Mathematics Subject Classification ID: 54C60
zbMATH DE Number: 5485404
zbMATH Keywords: multi-valued weak contraction
zbMATH Keywords: single-valued contractive mappings
zbMATH Keywords: \(b\)-metric space
author: Memudu Olaposi Olatinwo
reviewed by: Billy E. Rhoades
MaRDI profile type: Publication
full work available at URL: s11533-008-0047-3
OpenAlex ID: W2147236099
cites work: Fixed point theory and applications
cites work: Q4423213
cites work: Q4470075
cites work: Q5705653
cites work: Q4663557
cites work: On a general class of multi-valued weakly Picard mappings
cites work: On Nonlinear Contractions
cites work: NONEXPANSIVE NONLINEAR OPERATORS IN A BANACH SPACE
cites work: Q4884981
cites work: Q4225413
cites work: Q4415378
cites work: Q4464356
cites work: Fixed points of generalized contractive multi-valued mappings
cites work: On Contractive Mappings
cites work: Q5733836
cites work: Q4131303
cites work: Q3728703
cites work: Q3738253
cites work: Q3791880
cites work: An Introduction to Metric Spaces and Fixed Point Theory
cites work: On the convergence of the Ishikawa iterates to a common fixed point for a pair of multi-valued mappings
cites work: On fixed point stability for set-valued contractive mappings with applications to generalized differential equations
cites work: A fixed point theorem for set valued mappings
cites work: Fixed point theorems for multivalued mappings on complete metric spaces
cites work: Multi-valued contraction mappings
cites work: Q3620605
cites work: A Comparison of Various Definitions of Contractive Mappings
cites work: Q4884921
cites work: Q3352117
cites work: Q4104575
cites work: Generalized contractions and applications
cites work: Q4780769
cites work: Q5708805
cites work: Q3706042
DOI: 10.2478/S11533-008-0047-3
description: scientific article; zbMATH DE number 5485404