Fixed Points of Single- and Set-Valued Mappings in Uniformly Convex Metric Spaces with No Metric Convexity

We study the existence of fixed points and convergence of iterates for asymptotic pointwise contractions in uniformly convex metric spaces. We also study the existence of fixed points for set-valued nonexpansive mappings in the same class of spaces. Our results do not assume convexity of the metric...

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Bibliographic Details
Published inFixed point theory and algorithms for sciences and engineering
Main Authors Espínola, Rafa, Fernández-León, Aurora, Piatek, Bozena
Format Journal Article
LanguageEnglish
Published New York Springer Nature B.V 01.01.2010
Subjects
Algorithms
Studies
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Summary:We study the existence of fixed points and convergence of iterates for asymptotic pointwise contractions in uniformly convex metric spaces. We also study the existence of fixed points for set-valued nonexpansive mappings in the same class of spaces. Our results do not assume convexity of the metric which makes a big difference when studying the existence of fixed points for set-valued mappings.
ISSN:2730-5422