Convergence theorems for equilibrium problem, variational inequality problem and countably infinite relatively quasi-nonexpansive mappings

In this paper, we introduce an iterative process which converges strongly to a common element of set of common fixed points of countably infinite family of closed relatively quasi- nonexpansive mappings, the solution set of generalized equilibrium problem and the solution set of the variational ineq...

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Bibliographic Details
Published in:Applied mathematics and computation Vol. 216; no. 12; pp. 3439 - 3449
Main Authors: Zegeye, Habtu, Ofoedu, Eric U., Shahzad, Naseer
Format: Journal Article
Language:English
Published: Amsterdam Elsevier Inc 15.08.2010
Elsevier
Subjects:
[formula omitted]-inverse strongly monotone mappings
Banach space
Calculus of variations and optimal control
Computation
Convergence
Equilibrium problem
Exact sciences and technology
Functional analysis
Global analysis, analysis on manifolds
Inequalities
Iterative methods
Mapping
Mathematical analysis
Mathematical models
Mathematics
Monotone mappings
Numerical analysis
Numerical analysis in abstract spaces
Numerical analysis. Scientific computation
Sciences and techniques of general use
Strong convergence
Strongly monotone mappings
Theorems
Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds
Variational inequality problems
γ -inverse strongly monotone mappings
Strongly monotone mappings
Monotone mappings
Strong convergence
Variational inequality problems
Equilibrium problem
Iterative process
γ-inverse strongly monotone mappings
Banach space
Inverse problem
Variational problem
Numerical analysis
Fix point
Variational inequality
Applied mathematics
ISSN:0096-3003, 1873-5649
Online Access:Get full text
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Summary:In this paper, we introduce an iterative process which converges strongly to a common element of set of common fixed points of countably infinite family of closed relatively quasi- nonexpansive mappings, the solution set of generalized equilibrium problem and the solution set of the variational inequality problem for a γ -inverse strongly monotone mapping in Banach spaces. Our theorems improve, generalize, unify and extend several results recently announced.
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
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content type line 23
ISSN:0096-3003
1873-5649
DOI:10.1016/j.amc.2010.02.054