Existence and iteration for a mixed equilibrium problem and a countable family of nonexpansive mappings in Banach spaces

DOI10.1016/j.camwa.2011.03.029zbMath1221.49003OpenAlexW2051736855MaRDI QIDQ639093

Prasit Cholamjiak, Suthep Suantai

Publication date: 18 September 2011

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

Full work available at URL: https://doi.org/10.1016/j.camwa.2011.03.029

zbMATH Keywords

fixed pointnonexpansive mappingBanach spacemetric projectionmixed equilibrium problem

Mathematics Subject Classification ID

Variational and other types of inequalities involving nonlinear operators (general) (47J20) 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) Existence theories for problems in abstract spaces (49J27)

Related Items

Iterative approximation methods for mixed equilibrium problems for a countable family of quasi-\(\phi\)-asymptotically nonexpansive multivalued mappings in Banach spaces, New generalized mixed equilibrium problem with respect to relaxed semi-monotone mappings in Banach spaces, Viscosity approximation method for system of variational inclusions problems and fixed-point problems of a countable family of nonexpansive mappings, Strong convergence theorems for mixed equilibrium problem and asymptotically \(I\)-nonexpansive mapping in Banach spaces, A viscosity approximation method for weakly relatively nonexpansive mappings by the sunny nonexpansive retractions in Banach spaces

Cites Work

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• A generalization of Tychonoff's fixed point theorem
• Strong convergence theorem for a generalized equilibrium problem and a nonexpansive mapping in a Hilbert space
• Some characterizations for a family of nonexpansive mappings and convergence of a generated sequence to their common fixed point
• Weak convergence theorems for nonexpansive mappings in Banach spaces
• On the convex approximation property and the asymptotic behavior of nonlinear contractions in Banach spaces
• An example concerning fixed points
• Equilibrium programming using proximal-like algorithms
• Projection and proximal point methods: Convergence results and counterexamples.
• Strong convergence theorems for nonexpansive mappings and nonexpansive semigroups.
• Approximation of common fixed points of a countable family of nonexpansive mappings in a Banach space
• Approximating fixed points of nonexpansive mappings in a Banach space by metric projections
• Strong convergence theorems by hybrid methods for families of nonexpansive mappings in Hilbert spaces
• A hybrid iterative scheme for mixed equilibrium problems and fixed point problems
• Strong convergence theorems by the hybrid method for families of nonexpansive mappings in Hilbert spaces
• Strong and weak convergence theorems for equilibrium problems and relatively nonexpansive mappings in Banach spaces
• Strong Convergence of Approximating Fixed Point Sequences for Nonexpansive Mappings
• Properties of Fixed-Point Sets of Nonexpansive Mappings in Banach Spaces
• A Weak-to-Strong Convergence Principle for Fejér-Monotone Methods in Hilbert Spaces
• Mean Value Methods in Iteration
• Convergence theorems for nonexpansive mappings and feasibility problems