Approximation methods for solving equilibrium problems and variational inequality problems of an infite family of nonexpansive mappings
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Publication Details
Author list: Rattana P., Tanutpanit T., Kumam P.
Publisher: Hikari
Publication year: 2010
Journal: International Journal of Mathematical Analysis (1312-8876)
Volume number: 4
Issue number: 41-44
Start page: 2121
End page: 2141
Number of pages: 21
ISSN: 1312-8876
Languages: English-Great Britain (EN-GB)
Abstract
In this paper, we introduce an iterative scheme by a modified hybrid extragradient method for finding a common element of the set of fixed points of a countable family of nonexpansive mappings, the set of solutions of an equilibrium problem and the set of solutions of the variational inequality for α-inverse-strongly monotone mappings in a real Hilbert space. We show that the iterative sequence converges strongly to a common element of the above three sets, which solves some fixed point problems, variational inequality problems and equilibrium problems by using the hybrid method in mathematical programming which are connected with optimization problems. The results extend and improve the recent result of Kumam [11], Shinzato and Takahashi [21], Tada and Takahashi [24] and Takahashi et. al. [27].
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