Modified block iterative algorithm for Quasi- ϕ-asymptotically nonexpansive mappings and equilibrium problem in banach spaces

The purpose of this paper is to propose a modified block iterative algorithm for find a common element of the set of common fixed points of an infinite family of quasi- ϕ-asymptotically nonexpansive mappings and the set of an equilibrium problem. Under suitable conditions, some strong convergence th...

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Bibliographic Details
Published in:Applied mathematics and computation Vol. 217; no. 18; pp. 7520 - 7530
Main Authors: Chang, Shih-sen, Chan, Chi Kin, Joseph Lee, H.W.
Format: Journal Article
Language:English
Published: Amsterdam Elsevier Inc 15.05.2011
Elsevier
Subjects:
Equilibrium problem
Exact sciences and technology
Functional analysis
Generalized projection
Global analysis, analysis on manifolds
Mathematical analysis
Mathematics
Modified block iterative algorithm
Numerical analysis
Numerical analysis. Scientific computation
Quasi- ϕ-asymptotically nonexpansive mapping
Quasi- ϕ-nonexpansive mapping
Relatively nonexpansive mapping
Sciences and techniques of general use
Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds
Modified block iterative algorithm
Equilibrium problem
Relatively nonexpansive mapping
Generalized projection
Quasi- ϕ-nonexpansive mapping
Quasi- ϕ-asymptotically nonexpansive mapping
Quasi-φ-nonexpansive mapping
Strong convergence
Iterative method
Banach space
Algorithm
Weak convergence
Quasi-φ-asymptotically nonexpansive mapping
Numerical analysis
Fix point
Applied mathematics
Fixed point space
ISSN:0096-3003, 1873-5649
Online Access:Get full text
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Summary:The purpose of this paper is to propose a modified block iterative algorithm for find a common element of the set of common fixed points of an infinite family of quasi- ϕ-asymptotically nonexpansive mappings and the set of an equilibrium problem. Under suitable conditions, some strong convergence theorems are established in a uniformly smooth and strictly convex Banach space with the Kadec–Klee property. As an application, at the end of the paper a numerical example is given. The results presented in the paper improve and extend the corresponding results in Qin et al. [Convergence theorems of common elements for equilibrium problems and fixed point problem in Banach spaces, J. Comput. Appl. Math., 225, 2009, 20–30], Zhou et al. [Convergence theorems of a modified hybrid algorithm for a family of quasi- ϕ-asymptotically nonexpansive mappings, J. Appl. Math. Compt., 17 March, 2009, doi:10.1007/s12190-009-0263-4], Takahashi and Zembayshi [Strong and weak convergence theorems for equilibrium problems and relatively nonexpansive mappings in Banach spaces, Nonlinear Anal., 70, 2009, 45–57], Wattanawitoon and Kumam [Strong convergence theorems by a new hybrid projection algorithm for fixed point problem and equilibrium problems of two relatively quasi-nonexpansive mappings, Nonlinear Anal. Hybrid Syst., 3, 2009, 11–20] and Matsushita and Takahashi [A strong convergence theorem for relatively nonexpansive mappings in Banach spaces, J. Approx. Theory, 134, 2005, 257–266] and others.
ISSN:0096-3003
1873-5649
DOI:10.1016/j.amc.2011.02.060