Iterative scheme for nonself generalized asymptotically quasi-nonexpansive mappings

DOI10.1016/j.amc.2008.08.027zbMath1163.65030OpenAlexW2083018107MaRDI QIDQ2378771

Qifei Liu, Lei Deng

Publication date: 14 January 2009

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.amc.2008.08.027

zbMATH Keywords

convergenceiterationuniformly convex Banach spacecommon fixed pointuniformly \(L\)-Lipschitziannonself generalized 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)

Related Items

Viscosity approximation methods and strong convergence theorems for the fixed point of pseudocontractive and monotone mappings in Banach spaces ⋮ Strong convergence of viscosity approximation methods for the fixed-point of pseudo-contractive and monotone mappings ⋮ Convergence of Mann's type iteration method for generalized asymptotically nonexpansive mappings ⋮ Unnamed Item ⋮ Unnamed Item ⋮ New iterations with errors for approximating common fixed points for two generalized asymptotically quasi-nonexpansive nonself-mappings ⋮ Strong convergence of Mann's type iteration method for an infinite family of generalized asymptotically nonexpansive nonself mappings in Hilbert 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 infinitely nonexpansive mappings in Hilbert space

Cites Work

• Weak and strong convergence of a scheme with errors for two nonexpansive mappings
• Strong and weak convergence theorems for common fixed points of nonself asymptotically nonexpansive mappings
• Weak and strong convergence of the Ishikawa iteration process with errors for two asymptotically nonexpansive mappings
• Convergence of iterates with errors of asymptotically quasi-nonexpansive mappings and applications
• Iteration sequences for asymptotically quasi-nonexpansive mapping with an error member of uniform convex Banach space.
• Fixed-point iteration processes for non-Lipschitzian mappings of asymptotically quasi-nonexpansive type
• Strong and weak convergence theorems for asymptotically nonexpansive mappings.
• Strong convergence of an implicit iteration process for a finite family of generalized asymptotically quasi-nonexpansive maps
• Weak and strong convergence to fixed points of asymptotically nonexpansive mappings
• Approximating fixed points by ishikawa iterates
• Inequalities in Banach spaces with applications
• Approximating Fixed Points of Nonexpansive Mappings
• Weak and strong convergence theorems for fixed points of asymptotically nonexpansive mappings
• Iterative sequences for asymptotically quasi-nonexpansive mappings with error member

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