A convergence theorem based on a hybrid relaxed extragradient method for generalized equilibrium problems and fixed point problems of a finite family of nonexpansive mappings
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Publication Details
Author list: Jaiboon C., Chantarangsi W., Kumam P.
Publisher: Elsevier
Publication year: 2010
Journal: Nonlinear Analysis: Hybrid Systems (1751-570X)
Volume number: 4
Issue number: 1
Start page: 199
End page: 215
Number of pages: 17
ISSN: 1751-570X
eISSN: 1878-7460
Languages: English-Great Britain (EN-GB)
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Abstract
The purpose of this paper is to consider a new hybrid relaxed extragradient method for finding a common element of the set of solutions of a generalized equilibrium problem, the set of fixed points of a finite family of nonexpansive mappings and the set of solutions of variational inequalities for an inverse-strongly monotone mapping in Hilbert spaces. Then, we prove a strong convergence theorem of the iterative sequence generated by the proposed iterative algorithm under some suitable conditions. Our results extend and improve the recent results of Cai and Hu [G. Cai, C.S. Hu, A hybrid approximation method for equilibrium and fixed point problems for a family of infinitely nonexpansive mappings and a monotone mapping, Nonlinear Anal. Hybrid Syst., 3(2009) 395-407], Kangtunyakarn and Suantai [A. Kangtunyakarn, S. Suantai, A new mapping for finding common solution of equilibrium problems and fixed point problems of finite family of nonexpansive mappings, Nonlinear Anal., 71(2009) 4448-4460] and Thianwan [S. Thianwan, Strong convergence theorems by hybrid methods for a finite family of nonexpansive mappings and inverse-strongly monotone mappings, Nonlinear Anal. Hybrid Syst., 3(2009) 605-614] and many others. ฉ 2009 Elsevier Ltd. All rights reserved.
Keywords
Generalized equilibrium problem
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