On the Structure of Minimal Sets of Relatively Nonexpansive Mappings

In this article, we study the structure of minimal sets of relatively non-expansive mappings. We consider the cyclic and the noncyclic cases and show that results alike to the celebrated Goebel-Karlovitz lemma for non-expansive self-mappings can be obtained for relatively non-expansive mappings.

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Bibliographic Details
Published inNumerical functional analysis and optimization Vol. 34; no. 8; pp. 845 - 860
Main Authors Espínola, Rafa, Gabeleh, Moosa
Format Journal Article
LanguageEnglish
Published Taylor & Francis Group 03.08.2013
Subjects
Best proximity point
Fixed point
Functional analysis
Mapping
Optimization
Property UC
Proximal normal structure
Relatively non-expansive mapping
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Summary:In this article, we study the structure of minimal sets of relatively non-expansive mappings. We consider the cyclic and the noncyclic cases and show that results alike to the celebrated Goebel-Karlovitz lemma for non-expansive self-mappings can be obtained for relatively non-expansive mappings.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
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ISSN:0163-0563
1532-2467
DOI:10.1080/01630563.2013.763824