Nonexpansive retractions in hyperconvex spaces
type: Item
instance of: scholarly article
title: Nonexpansive retractions in hyperconvex spaces
zbMATH Open document ID: 0971.47036
published in: Journal of Mathematical Analysis and Applications
publication date: 2001-11-04T00:00:00Z
review text: This article deals with nonexpansive retractions on a hyperconvex subsets \(D\) of a hyperconvex metric space \(M\). The authors investigate the problems of existence of retractions \(R\) of \(M\) onto \(D\) with the property \(R(M\setminus D)\subseteq\partial D\) or \(d(x,R(x))= \text{dist}(x,D)\) \((x\in M)\). In particular, they prove that a externally hyperconvex relative to \(M\) in some weak sense subset \(D\) with an empty interior a nonexpansive retraction of \(M\) such that \(R(M\setminus D)\subseteq\partial D\) and that for any compact weakly externally hyperconvex subset \(D\) there exists a nonexpansive retraction \(R\) of \(M\) onto \(M\) such that \(d(x,R(x))= \text{dist}(x,D)\) \((x\in M)\).
Mathematics Subject Classification ID: 47H09
zbMATH DE Number: 1556932
zbMATH Keywords: nonexpansive retractions
zbMATH Keywords: hyperconvex subsets
author: Rafa Espínola
author: W. A. Kirk
author: Genaro López
reviewed by: Peter P. Zabreĭko
MaRDI profile type: Publication
full work available at URL: jmaa.2000.7030
OpenAlex ID: W1998191468
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DOI: 10.1006/JMAA.2000.7030
description: scientific article; zbMATH DE number 1556932