Title of article :
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
Author/Authors :
Jaiboon، نويسنده , , Chaichana and Chantarangsi، نويسنده , , Wanpen and Kumam، نويسنده , , Poom، نويسنده ,
Issue Information :
روزنامه با شماره پیاپی سال 2010
Pages :
17
From page :
199
To page :
215
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.
Keywords :
Generalized equilibrium problem , Variational inequality , Nonexpansive mapping , Inverse-strongly monotone mapping , Fixed point
Journal title :
Nonlinear Analysis Hybrid Systems
Serial Year :
2010
Journal title :
Nonlinear Analysis Hybrid Systems
Record number :
1602381
Link To Document :
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