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Zbl 1179.49011
Jaiboon, Chaichana; Chantarangsi, Wanpen; Kumam, Poom
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. (English)
[J] Nonlinear Anal., Hybrid Syst. 4, No. 1, 199-215 (2010). ISSN 1751-570X

Summary: 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 {\it G. Cai} and {\it C. S. Hu} [Nonlinear Anal., Hybrid Syst. 3, No.~4, 395--407 (2009; Zbl 1223.47071)], {\it A. Kangtunyakarn} and {\it S. Suantai} [Nonlinear Anal., Theory Methods Appl. 71, No.~10 (A), 4448--4460 (2009; Zbl 1167.47304)] and {\it S. Thianwan} [Nonlinear Anal., Hybrid Syst. 3, No.~4, 605--614 (2009; Zbl 1219.49008)] and many others.

MSC 2000:: *49J40 Variational methods including variational inequalities
49M30 Methods of successive approximation, not based on necessary cond.
47H09 Mappings defined by "shrinking" properties

Keywords: generalized equilibrium problem; fixed point; variational inequality; nonexpansive mapping; inverse-strongly monotone mapping

Citations: Zbl 1167.47304; Zbl 1223.47071

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