Weak and strong convergence theorems for a finite family of generalized asymptotically quasi-nonexpansive mappings

DOI10.1016/j.camwa.2010.07.025zbMath1205.65186OpenAlexW2035591365MaRDI QIDQ623115

Watcharaporn Cholamjiak, Suthep Suantai

Publication date: 13 February 2011

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.camwa.2010.07.025

zbMATH Keywords

strong convergenceiterative methodBanach spacecommon fixed pointgeneralized asymptotically quasi-nonexpansive mapping

Mathematics Subject Classification ID

Iterative procedures involving nonlinear operators (47J25) Fixed-point theorems (47H10) Contraction-type mappings, nonexpansive mappings, (A)-proper mappings, etc. (47H09) Numerical solutions to equations with nonlinear operators (65J15)

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Viscosity approximation method for generalized asymptotically quasi-nonexpansive mappings in a convex metric space

Cites Work

• Iterative construction of fixed points of asymptotically nonexpansive mappings
• A new three-step fixed point iteration scheme for asymptotically nonexpansive mappings
• Convergence of iterates with errors of asymptotically quasi-nonexpansive mappings and applications
• Approximation of common fixed points of families of nonexpansive mappings
• An implicit iterative scheme for monotone variational inequalities and fixed point problems
• Convergence of a general iterative scheme for a finite family of asymptotically quasi-nonexpansive mappings in convex metric spaces and applications
• Implicit iteration scheme with perturbed mapping for equilibrium problems and fixed point problems of finitely many nonexpansive mappings
• Strong convergence of an implicit iteration process for a finite family of generalized asymptotically quasi-nonexpansive maps
• Common fixed points Noor iteration for a finite family of asymptotically quasi-nonexpansive mappings in Banach spaces
• Weak and strong convergence criteria of Noor iterations for asymptotically nonexpansive mappings
• Approximating common fixed points of asymptotically quasi-nonexpansive mappings by a \(k+1\)-step iterative scheme with error terms
• Inequalities in Banach spaces with applications
• Weak convergence of the sequence of successive approximations for nonexpansive mappings
• Weak and strong convergence theorems for fixed points of asymptotically nonexpansive mappings

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