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 -