Nonexpansive mappings in metric and Banach spaces

DOI10.1007/BF02924816zbMath0519.54029OpenAlexW2019913860MaRDI QIDQ3668478

William A. Kirk

Publication date: 1981

Published in: Rendiconti del Seminario Matematico e Fisico di Milano (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02924816

zbMATH Keywords

nonexpansive mappingsBrowder-Goehde demiclosedness principlemetric space possessing a convexity structure

Mathematics Subject Classification ID

Fixed-point theorems (47H10) Fixed-point and coincidence theorems (topological aspects) (54H25) Contraction-type mappings, nonexpansive mappings, (A)-proper mappings, etc. (47H09) Fuzzy topology (54A40)

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Cites Work

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• A simple proof of the mean ergodic theorem for nonlinear contractions in Banach spaces
• Weak convergence theorems for nonexpansive mappings in Banach spaces
• Strong convergence theorems for resolvents of accretive operators in Banach spaces
• Asymptotic centers and nonexpansive mappings in conjugate Banach spaces
• On the convex approximation property and the asymptotic behavior of nonlinear contractions in Banach spaces
• An elementary proof of the fixed-point theorem of Browder and Kirk
• A Convexity Condition in Banach Spaces and the Strong Law of Large Numbers
• On nonlinear contraction semigroups in sup norm spaces
• An Abstract Fixed Point Theorem for Nonexpansive Mappings
• Strong and weak convergence theorems for locally nonexpansive mappings in Banach spaces
• Existence of Fixed Points of Nonexpansive Mappings in Certain Banach Lattices
• Zum Prinzip der kontraktiven Abbildung
• NONEXPANSIVE NONLINEAR OPERATORS IN A BANACH SPACE
• A Fixed Point Theorem for Mappings which do not Increase Distances
• Semicontractive and semiaccretive nonlinear mappings in Banach spaces
• Normed Linear Spaces that are Uniformly Convex in Every Direction