Strong convergence of an explicit iteration process for a totally asymptotically \(I\)-nonexpansive mapping in Banach spaces

DOI10.1016/j.aml.2010.08.016zbMath1201.47064OpenAlexW2066338791MaRDI QIDQ602837

Farrukh Mukhamedov, Mansoor Saburov

Publication date: 5 November 2010

Published in: Applied Mathematics Letters (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.aml.2010.08.016

zbMATH Keywords

strong convergenceuniformly convex Banach spacecommon fixed pointiteration processtotally asymptotically \(I\)-nonexpansive mappingtotally asymptotically nonexpansive mapping

Mathematics Subject Classification ID

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

Related Items (11)

Fixed Point of A New Type Nonself Total Asymptotically Nonexpansive Mappings in Banach Spaces ⋮ Modified Picard-Mann hybrid iteration process for total asymptotically nonexpansive mappings ⋮ Generalized nearly asymptotically nonexpansive mappings and a system of generalized variational-like inclusions: iterative method and approximation of common solutions ⋮ Iterative algorithm for fixed point problems of generalized nearly asymptotically nonexpansive mappings and solutions of a system of generalized nonlinear variational-like inclusions ⋮ A proximal iterative algorithm for system of generalized nonlinear variational-like inequalities and fixed point problems ⋮ Strong convergence of non-implicit iteration process with errors in Banach spaces ⋮ System of generalized variational-like inclusions involving \((P,\eta)\)-accretive mapping and fixed point problems in real Banach spaces ⋮ Generalized set-valued nonlinear variational-like inequalities and fixed point problems: existence and approximation solvability results ⋮ Variational inclusion problem and total asymptotically nonexpansive mapping: graph convergence, algorithms and approximation of common solutions ⋮ Unnamed Item ⋮ Unnamed Item

Cites Work

• Unnamed Item
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• Approximation of common fixed points for finite families of total asymptotically nonexpansive mappings
• A new iteration process for approximation of common fixed points for finite families of total asymptotically nonexpansive mappings
• Weak and strong convergence of an implicit iteration process for an asymptotically quasi-I-nonexpansive mapping in Banach space
• On the convergence theorems of implicit iteration process for a finite family of \(I\)-asymptotically nonexpansive mappings
• Approximating fixed points of nonexpansive mappings by the Ishikawa iteration process
• Fixed point theorems for non-Lipschitzian mappings of asymptotically nonexpansive type
• Approximating fixed points of total asymptotically nonexpansive mappings
• Geometric properties of Banach spaces and nonlinear iterations
• Weak and strong convergence to fixed points of asymptotically nonexpansive mappings
• Convergence of iterates of asymptotically nonexpansive mappings in Banach spaces with the uniform Opial property
• GENERALIZED I-NONEXPANSIVE MAPS AND BEST APPROXIMATIONS IN BANACH SPACES
• A Fixed Point Theorem for Asymptotically Nonexpansive Mappings

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