Nonexpansive mappings defined on unbounded domains
type: Item
instance of: scholarly article
title: Nonexpansive mappings defined on unbounded domains
zbMATH Open document ID: 1141.47036
DOI: 10.1155/FPTA/2006/82080
published in: Fixed Point Theory and Applications
publication date: 2007-06-13T00:00:00Z
full work available at URL: https://eudml.org/doc/54355
review text: The authors study the existence of fixed points for nonexpansive mappings when their domains are unbounded. The main result of this part of the article parallels a corresponding result due to \textit{R. E. Bruck jun.} [Trans. Am. Math. Soc. 179, 251--262 (1973; Zbl 0265.47043)] in the bounded case, and it relies heavily on the results of Bruck. Several fixed point theorems for nonexpansive mappings involve mappings \(f : C \to X\) in conjunction with boundary and inwardness conditions. It is customary in these results to assume that the domain \(C\) is bounded. Finally, the authors consider fixed point theorems for mappings \(f:C\to X\), where \(C\) is not necessarily bounded, which are nonexpansive or continuous pseudocontractive in conjunction with satisfy Leray-Schauder-type boundary conditions.
reviewed by: Poom Kumam
Mathematics Subject Classification ID: 47H09
Mathematics Subject Classification ID: 47H10
zbMATH DE Number: 5164031
zbMATH Keywords: nonexpansive mappings
zbMATH Keywords: asymptotically contractive
zbMATH Keywords: radially asymptotically contractive
zbMATH Keywords: nonexpansive retract
zbMATH Keywords: fixed point property
Wikidata QID: Q59212405
author: Anchalee Kaewcharoen
author: W. A. Kirk
MaRDI profile type: Publication
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OpenAlex ID: W2132005784
description: scientific article; zbMATH DE number 5164031