A hybrid approximation algorithm for finding common solutions of equilibrium problems, a finite family of variational inclusions, and fixed point problems in Hilbert spaces

In this paper, we introduce an iterative method for finding a common element of the set of fixed points of nonexpansive mappings, the set of solutions of a finite family of variational inclusions with set-valued maximal monotone mappings and inverse strongly monotone mappings, and the set of solutio...

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Bibliographic Details
Published in:Journal of inequalities and applications Vol. 2013; no. 1; pp. 1 - 16
Main Authors: Deng, Bin-Chao, Chen, Tong
Format: Journal Article
Language:English
Published: Cham Springer International Publishing 01.12.2013
Springer Nature B.V
Subjects:
Analysis
Applications of Mathematics
Approximation
Convergence
Fixed points (mathematics)
Hilbert space
Inclusions
Inequalities
Inverse
Mapping
Mathematical analysis
Mathematics
Mathematics and Statistics
inverse strongly monotone
maximal monotone mapping
fixed point
equilibrium problem
variational inclusions
ISSN:1029-242X, 1025-5834, 1029-242X
Online Access:Get full text
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Summary:In this paper, we introduce an iterative method for finding a common element of the set of fixed points of nonexpansive mappings, the set of solutions of a finite family of variational inclusions with set-valued maximal monotone mappings and inverse strongly monotone mappings, and the set of solutions of an equilibrium problem in Hilbert spaces. Furthermore, using our new iterative scheme, under suitable conditions, we prove some strong convergence theorems for approximating these common elements. The results presented in the paper improve and extend many recent important results.
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ISSN:1029-242X
1025-5834
1029-242X
DOI:10.1186/1029-242X-2013-165