On Reich's strong convergence theorem for asymptotically nonexpansive mappings in Banach spaces

DOI10.1016/j.na.2006.03.025zbMath1123.47045OpenAlexW2089615502MaRDI QIDQ878516

Chi Kin Chan, Shi Sheng Zhang, H. W. Joseph Lee

Publication date: 26 April 2007

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.2006.03.025

zbMATH Keywords

fixed pointasymptotically nonexpansive mappingiterative schemeBanach spaceapproximate fixed point sequenceconvergence theorem

Mathematics Subject Classification ID

Iterative procedures involving nonlinear operators (47J25) Fixed-point theorems (47H10) Contraction-type mappings, nonexpansive mappings, (A)-proper mappings, etc. (47H09)

Related Items

Approximation of fixed points of nonexpansive mapping in Banach spaces ⋮ Viscosity approximation methods and strong convergence theorems for the fixed point of pseudocontractive and monotone mappings in Banach spaces ⋮ A generalization and improvement of Chidume theorems for total asymptotically nonexpansive mappings in Banach spaces ⋮ Approximation of common fixed points for finite families of total asymptotically nonexpansive mappings ⋮ Strong convergence of viscosity approximation methods for the fixed-point of pseudo-contractive and monotone mappings ⋮ Weak and strong convergence theorems for finite families of asymptotically quasi-nonexpansive mappings in Banach spaces ⋮ Viscosity approximation methods with errors and strong convergence theorems for a common point of pseudocontractive and monotone mappings: solutions of variational inequality problems ⋮ Strong convergence theorems for three-steps iterations for asymptotically nonexpansive mappings in Banach spaces ⋮ Mixed approximation for nonexpansive mappings in Banach spaces ⋮ A new iteration process for approximation of common fixed points for finite families of total asymptotically nonexpansive mappings ⋮ Strong convergence theorems on a viscosity approximation method for a finite family of pseudo-contractive mappings in Banach spaces

Cites Work

• Unnamed Item
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• Viscosity approximation methods for a finite family of nonexpansive mappings in Banach spaces
• On Reich's strong convergence theorems for resolvents of accretive operators
• Strong convergence theorems for resolvents of accretive operators in Banach spaces
• On the asymptotic behavior of nonlinear semigroups and the range of accretive operators
• Approximation of fixed points of nonexpansive mappings
• On Chidume's open questions and approximate solutions of multivalued strongly accretive mapping equations in Banach spaces
• Ishikawa and Mann iterative process with errors for nonlinear strongly accretive mappings in Banach spaces
• Some problems and results in fixed point theory
• Strong convergence of approximated sequences for nonexpansive mappings in Banach spaces
• Convergence of paths for pseudo-contractive mappings in Banach spaces
• Positivity of duality mappings
• A Fixed Point Theorem for Asymptotically Nonexpansive Mappings