TY - JOUR

T1 - Hybrid iterative method for finding common solutions of generalized mixed equilibrium and fixed point problems

AU - Ceng, Lu Chuan

AU - Guu, Sy Ming

AU - Yao, Jen Chih

PY - 2012

Y1 - 2012

N2 - Recently, Colao et al. (J Math Anal Appl 344:340-352, 2008) introduced a hybrid viscosity approximation method for finding a common element of the set of solutions of an equilibrium problem and the set of fixed points of a finite family of nonexpansive mappings in a real Hilbert space. In this paper, by combining Colao, Marino and Xu's hybrid viscosity approximation method and Yamada's hybrid steepest-descent method, we propose a hybrid iterative method for finding a common element of the set GMEP of solutions of a generalized mixed equilibrium problem and the set ∩Ni=1 Fix (S i) of fixed points of a finite family of nonexpansive mappings {Si}Ni = 1 in a real Hilbert space. We prove the strong convergence of the proposed iterative algorithm to an element of ∩Ni=1 Fix (Si) ∩ GMEP, which is the unique solution of a variational inequality.

AB - Recently, Colao et al. (J Math Anal Appl 344:340-352, 2008) introduced a hybrid viscosity approximation method for finding a common element of the set of solutions of an equilibrium problem and the set of fixed points of a finite family of nonexpansive mappings in a real Hilbert space. In this paper, by combining Colao, Marino and Xu's hybrid viscosity approximation method and Yamada's hybrid steepest-descent method, we propose a hybrid iterative method for finding a common element of the set GMEP of solutions of a generalized mixed equilibrium problem and the set ∩Ni=1 Fix (S i) of fixed points of a finite family of nonexpansive mappings {Si}Ni = 1 in a real Hilbert space. We prove the strong convergence of the proposed iterative algorithm to an element of ∩Ni=1 Fix (Si) ∩ GMEP, which is the unique solution of a variational inequality.

KW - Fixed point

KW - Generalized mixed equilibrium problem

KW - Hybrid iterative method

KW - Nonexpansive mapping

KW - Variational inequality

UR - http://www.scopus.com/inward/record.url?scp=84873862186&partnerID=8YFLogxK

U2 - 10.1186/1687-1812-2012-92

DO - 10.1186/1687-1812-2012-92

M3 - 文章

AN - SCOPUS:84873862186

SN - 1687-1820

VL - 2012

JO - Fixed Point Theory and Applications

JF - Fixed Point Theory and Applications

M1 - 92

ER -