Some computational aspects of metric fixed-point theory

DOI10.1016/j.na.2005.01.075zbMath1086.47021OpenAlexW2086045987MaRDI QIDQ1775881

Ulrich Kohlenbach

Publication date: 4 May 2005

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.na.2005.01.075

zbMATH Keywords

fixed pointcomputable analysisnonexpansive operatorKrasnoselskij-Mann iteration

Mathematics Subject Classification ID

Iterative procedures involving nonlinear operators (47J25) Fixed-point theorems (47H10) Fixed-point and coincidence theorems (topological aspects) (54H25) Contraction-type mappings, nonexpansive mappings, (A)-proper mappings, etc. (47H09) Functionals in proof theory (03F10)

Related Items (13)

Best Proximity Pair Results for Relatively Nonexpansive Mappings in Geodesic Spaces ⋮ Convergence analysis of a general iteration schema of nonlinear mappings in hyperbolic spaces ⋮ A note on the finitization of Abelian and Tauberian theorems ⋮ Quantitative results on Fejér monotone sequences ⋮ Strong Convergence for the Alternating Halpern–Mann Iteration in CAT(0) Spaces ⋮ Bounds on Kuhfittig's iteration schema in uniformly convex hyperbolic spaces ⋮ The cohesive principle and the Bolzano-Weierstraß principle ⋮ A functional interpretation for nonstandard arithmetic ⋮ General logical metatheorems for functional analysis ⋮ Metastability of the proximal point algorithm with multi-parameters ⋮ Quantitative translations for viscosity approximation methods in hyperbolic spaces ⋮ A new metastable convergence criterion and an application in the theory of uniformly convex Banach spaces ⋮ Asymptotic regularity, fixed points and successive approximations

Cites Work

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• A note on segmenting Mann iterates
• A QUANTITATIVE VERSION OF A THEOREM DUE TO BORWEIN-REICH-SHAFRIR
• Iteration processes for nonexpansive mappings
• Krasnoselski-Mann Iterations in Normed Spaces
• Nonexpansive iterations in hyperbolic spaces
• Approximate fixed points for nonexpansive mappings in uniformly convex spaces
• Nonexpansive Mappings, Asymptotic Regularity and Successive Approximations
• Fixed Points and Iteration of a Nonexpansive Mapping in a Banach Space
• Krasnoselskii's iteration process in hyperbolic space
• Some logical metatheorems with applications in functional analysis
• General logical metatheorems for functional analysis
• A Fixed Point Theorem for Asymptotically Nonexpansive Mappings
• Fixed points and approximate fixed points in product spaces

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