A hybrid iterative scheme for mixed equilibrium problems and fixed point problems

The purpose of this paper is to investigate the problem of finding a common element of the set of solutions of a mixed equilibrium problem (MEP) and the set of common fixed points of finitely many nonexpansive mappings in a real Hilbert space. First, by using the well-known KKM technique we derive t...

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Bibliographic Details
Published in:Journal of computational and applied mathematics Vol. 214; no. 1; pp. 186 - 201
Main Authors: Ceng, Lu-Chuan, Yao, Jen-Chih
Format: Journal Article
Language:English
Published: Amsterdam Elsevier B.V 15.04.2008
Elsevier
Subjects:
[formula omitted]-Strongly convex functions
Exact sciences and technology
Functional analysis
Global analysis, analysis on manifolds
Hilbert spaces
Hybrid iterative schemes
KKM mappings
Mathematical analysis
Mathematics
Mixed equilibrium problems
Nonexpansive mappings
Numerical analysis
Numerical analysis. Scientific computation
Sciences and techniques of general use
Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds
47H10
Mixed equilibrium problems
49J30
90C99
Hilbert spaces
Hybrid iterative schemes
47H17
η -Strongly convex functions
Nonexpansive mappings
KKM mappings
Solution uniqueness
49J30; 47H10; 47H17; 90C99
Numerical analysis
Fix point
Existence of solution
Applied mathematics
Iterative method
Hilbert space
Convex function
Mixed problem
Mixed equilibrium problems; Hybrid iterative schemes; η-Strongly convex functions; KKM mappings; Nonexpansive mappings; Hilbert spaces
ISSN:0377-0427, 1879-1778
Online Access:Get full text
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Summary:The purpose of this paper is to investigate the problem of finding a common element of the set of solutions of a mixed equilibrium problem (MEP) and the set of common fixed points of finitely many nonexpansive mappings in a real Hilbert space. First, by using the well-known KKM technique we derive the existence and uniqueness of solutions of the auxiliary problems for the MEP. Second, by virtue of this result we introduce a hybrid iterative scheme for finding a common element of the set of solutions of MEP and the set of common fixed points of finitely many nonexpansive mappings. Furthermore, we prove that the sequences generated by the hybrid iterative scheme converge strongly to a common element of the set of solutions of MEP and the set of common fixed points of finitely many nonexpansive mappings.
ISSN:0377-0427
1879-1778
DOI:10.1016/j.cam.2007.02.022