Remarks on asymptotic centers and fixed points
type: Item
instance of: scholarly article
title: Remarks on asymptotic centers and fixed points
zbMATH Open document ID: 1213.46019
DOI: 10.1155/2010/247402
author: Juan-Miguel Gracia
published in: Abstract and Applied Analysis
publication date: 2011-02-09T00:00:00Z
full work available at URL: https://eudml.org/doc/231343
review text: Summary: We introduce a class of nonlinear continuous mappings defined on a bounded closed convex subset of a Banach space \(X\). We characterize the Banach spaces in which every asymptotic center of each bounded sequence in any weakly compact convex subset is compact as those spaces having the weak fixed point property for this type of mappings.
Mathematics Subject Classification ID: 46B20
Mathematics Subject Classification ID: 47H09
Mathematics Subject Classification ID: 47H10
zbMATH DE Number: 5848803
zbMATH Keywords: asymptotic center
zbMATH Keywords: weak fixed point property
Wikidata QID: Q58649795
MaRDI profile type: Publication
OpenAlex ID: W2060653772
cites work: The construction of an asymptotic center with a fixed-point property
cites work: Q3353650
cites work: Edelstein's method and fixed point theorems for some generalized nonexpansive mappings
cites work: Q3998720
cites work: The fixed point property for mappings admitting a center
cites work: Properties of Fixed-Point Sets of Nonexpansive Mappings in Banach Spaces
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description: scientific article; zbMATH DE number 5848803