Fixed point theorem on two complete cone metric spaces
type: Item
instance of: scholarly article
title: Fixed point theorem on two complete cone metric spaces
zbMATH Open document ID: 1401.54027
author: Xianjiu Huang
author: Xi Wen
author: Chuanxi Zhu
published in: Annali dell'Università di Ferrara. Sezione VII. Scienze Matematiche
publication date: 2012-11-15T00:00:00Z
review text: Let \((X,d_1)\) and \((Y,d_2)\) be two cone metric spaces in the sense of [\textit{L.-G. Huang} and \textit{X. Zhang}, J. Math. Anal. Appl. 332, No. 2, 1468--1476 (2007; Zbl 1118.54022)] and let \(T:X\to Y\) and \(S:Y\to X\) be two mappings such that, for \(x\in X\) and \(y\in Y\), there exist \[ u\in\{d_1(x,Sy),d_2(y,Tx),d_2(y,TSy)\} \] and \[ v\in\{d_2(y,Tx),d_1(x,Sy),d_1(x,STx)\} \] satisfying \[ d_2(Tx,TSy)\leq\lambda u \] and \[ d_1(Sy,STx)\leq\lambda v, \] where \(0<\lambda<1\). The authors prove that \(ST\) and \(TS\) have unique fixed points in \(X\) and \(Y\), respectively. A similar assertion is proved when four mappings are given. An example is provided to demonstrate the use of these results.
reviewed by: Zoran Kadelburg
Mathematics Subject Classification ID: 54H25
Mathematics Subject Classification ID: 47H10
zbMATH DE Number: 6107672
zbMATH Keywords: cone metric space
zbMATH Keywords: related fixed point theorem
zbMATH Keywords: complete space
MaRDI profile type: Publication
full work available at URL: s11565-011-0125-5
OpenAlex ID: W2001438274
cites work: Common fixed point results for noncommuting mappings without continuity in cone metric spaces
cites work: Fixed and periodic point results in cone metric spaces
cites work: Fixed point theorems for set-valued mappings of contractive type
cites work: Q4380213
cites work: Q3925540
cites work: Q3966772
cites work: Cone metric spaces and fixed point theorems of contractive mappings
cites work: Pre-image entropy of nonautonomous dynamical systems
cites work: Q2930457
cites work: Common fixed point theorem for four non-self mappings in cone metric spaces
cites work: Common fixed points for maps on cone metric space
cites work: Common fixed point theorems for weakly compatible pairs on cone metric spaces
cites work: Some Remarks Concerning Contraction Mappings
cites work: Some notes on the paper ``Cone metric spaces and fixed point theorems of contractive mappings''
cites work: A Comparison of Various Definitions of Contractive Mappings
cites work: Common fixed points in cone metric spaces
cites work: Endpoints and fixed points of set-valued contractions in cone metric spaces
cites work: Q5686501
cites work: Q4456226
cites work: Random ambiguous point of random \(k(\omega )\)-set-contractive operator
cites work: Calculations of random fixed point index
DOI: 10.1007/S11565-011-0125-5
description: scientific article; zbMATH DE number 6107672