A QUANTITATIVE VERSION OF A THEOREM DUE TO BORWEIN-REICH-SHAFRIR

DOI10.1081/NFA-100105311zbMath1001.47035OpenAlexW2016012858MaRDI QIDQ2769522

Ulrich Kohlenbach

Publication date: 16 December 2002

Published in: Numerical Functional Analysis and Optimization (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1081/nfa-100105311

zbMATH Keywords

nonexpansive mapuniform upper boundsKrasnosel'skij-Mann iterations

Mathematics Subject Classification ID

Iterative procedures involving nonlinear operators (47J25) Constructive and recursive analysis (03F60) Fixed-point theorems (47H10) Contraction-type mappings, nonexpansive mappings, (A)-proper mappings, etc. (47H09) Functionals in proof theory (03F10)

Related Items (17)

Proof mining in \(L_{1}\)-approximation ⋮ Uniform asymptotic regularity for Mann iterates. ⋮ A quadratic rate of asymptotic regularity for CAT(0)-spaces ⋮ Rates of Convergence for Asymptotically Weakly Contractive Mappings in Normed Spaces ⋮ Some logical metatheorems with applications in functional analysis ⋮ Asymptotic behavior of averaged and firmly nonexpansive mappings in geodesic spaces ⋮ A computational study of a class of recursive inequalities ⋮ Rates of convergence for iterative solutions of equations involving set-valued accretive operators ⋮ Averaged alternating reflections in geodesic spaces ⋮ Bounds on Kuhfittig's iteration schema in uniformly convex hyperbolic spaces ⋮ Quantitative image recovery theorems ⋮ Bounded functional interpretation ⋮ Effective rates of convergence for Lipschitzian pseudocontractive mappings in general Banach spaces ⋮ On the rate of convergence of Krasnosel'skiĭ-Mann iterations and their connection with sums of Bernoullis ⋮ Some computational aspects of metric fixed-point theory ⋮ 2003 Annual Meeting of the Association for Symbolic Logic ⋮ General logical metatheorems for functional analysis

Cites Work

• Effective moduli from ineffective uniqueness proofs. An unwinding of de La Vallée Poussin's proof for Chebycheff approximation
• Nonexpansive mappings and asymptotic regularity
• Krasnoselski-Mann Iterations in Normed Spaces
• Nonexpansive iterations in hyperbolic spaces
• A critique of numerical analysis
• Nonexpansive Mappings, Asymptotic Regularity and Successive Approximations
• New effective moduli of uniqueness and uniform a priori estimates for constants of strong unicity by logical analysis of known proofs in best approximation theory
• Zum Prinzip der kontraktiven Abbildung
• NONEXPANSIVE NONLINEAR OPERATORS IN A BANACH SPACE
• A Fixed Point Theorem for Mappings which do not Increase Distances
• Convergence of Krasnoselskii-Mann iterations of nonexpansive operators
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