Some fixed point theorems in Banach space
type: Item
instance of: scholarly article
title: Some fixed point theorems in Banach space
zbMATH Open document ID: 0671.47053
DOI: 10.1016/0022-247X(89)90309-0
author: T. H. Chang
author: Chi-Lin Yen
published in: Journal of Mathematical Analysis and Applications
publication date: 1989-01-01T00:00:00Z
review text: Theorem 1. Let K be a nonempty weakly compact convex subset of a Banach space X, and \(T:K\to 2^ x\) be a mapping such that the mapping \(x\to d(x,Tx)\) is lower semicontinuous. If inf \(\{\) d(x,Tx);x\(\in K\}=0\) and for all \(x,y\in K\), \(0\leq \lambda \leq 1\), \(u=\lambda x+(1-\lambda)y\) we have d(u,Tu)\(\leq \phi (\max [d(x,Tx),d(y,Ty)])\), where \(\phi:{\mathbb{R}}^+\to {\mathbb{R}}^+\) is nondecreasing, continuous from the right at 0 with \(\phi (0)=0\), \(d(x,Tx)=\inf \{\| x-y\|,y\in Tx\}\). Then T has a fixed point. From this theorem the authors deduce some well known fixed point theorem in Banach space.
Mathematics Subject Classification ID: 47H10
zbMATH DE Number: 4098120
zbMATH Keywords: weakly compact convex subset of a Banach space
zbMATH Keywords: lower semicontinuous
zbMATH Keywords: fixed point theorem in Banach space
reviewed by: Alexandra Rodkina
MaRDI profile type: Publication
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full work available at URL: 0022-247x(89)90309-0
OpenAlex ID: W2076463990
description: scientific article; zbMATH DE number 4098120