A common fixed point theorem for a class of mappings
type: Item
instance of: scholarly article
title: A common fixed point theorem for a class of mappings
zbMATH Open document ID: 0533.54031
published in: Indian Journal of Pure \& Applied Mathematics
publication date: 1983-01-01T00:00:00Z
review text: The authors have proved the following theorem. Theorem. Let A be a selfmapping of X, and S and T be continuous selfmappings on X satisfying the following conditions: (I) \(\{A,S\}\) and \(\{A,T\}\) are weakly commuting pairs such that \(A(X)\subset S(X)\cap T(X);\) (II) there exists a \(\phi\in\Psi\) such that for all \(x,y\in X\) \[ d(Ax,Ay) \leq \phi(d(Sx,Ty), d(Sx,Ax), d(Sx,Ay), d(Ty,Ax), d(Ty,Ay)) \] where \(\phi\) satisfies (III) for any \(t>0\), \(\phi(t,t,a_ 1t,a_ 2t,t)<t,\) where \(a_ 1+a_ 2=3.\) Then A, S and T have a unique common fixed point in X.
Mathematics Subject Classification ID: 54H25
zbMATH DE Number: 3846457
zbMATH Keywords: complete metric space
zbMATH Keywords: weakly commuting pair
zbMATH Keywords: common fixed point
author: M. S. Khan
author: Mohammad Imdad
reviewed by: J. Achari
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 3846457