A short survey on open problems in metric fixed point theory and some related results for nonexpansive mappings
type: Item
instance of: scholarly article
title: A short survey on open problems in metric fixed point theory and some related results for nonexpansive mappings
zbMATH Open document ID: 1490.46012
author: Gopal Dutta
author: P. Veeramani
published in: The Journal of Analysis
publication date: 2021-08-19T00:00:00Z
review text: Let \(K\) be a nonempty closed bounded convex subset of a normed linear space \(X:=(X,{\|\cdot\|})\). We say that \(K\) has the fixed point property if every nonexpansive mapping \(T:K\to K\), that is, \(\|Tx-Ty\|\le\|x-y\|\) for all \(x,y\in K\), has a fixed point. We also say that \(X\) has the fixed point property (weak fixed point property, resp.) if every closed bounded convex subset (weakly compact convex subset, resp.) of \(X\) has the fixed point property. In this paper, the authors discuss various sufficient conditions for the fixed point property and the weak fixed point property of a Banach space.
reviewed by: Satit Saejung
Mathematics Subject Classification ID: 46B20
Mathematics Subject Classification ID: 47H09
Mathematics Subject Classification ID: 47H10
Mathematics Subject Classification ID: 00A27
zbMATH DE Number: 7383682
zbMATH Keywords: nonexpansive mappings
zbMATH Keywords: fixed point property
MaRDI profile type: Publication
full work available at URL: s41478-019-00200-5
OpenAlex ID: W2973979321
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Wikidata QID: Q127233224
DOI: 10.1007/S41478-019-00200-5
description: scientific article; zbMATH DE number 7383682