Viscosity Approximation Methods for Generalized Equilibrium Problems and Fixed Point Problems of Finite Family of Nonexpansive Mappings in Hilbert Spaces
Utith Inprasit · Thai Journal of Mathematics · 2012
In this paper, we introduce an iterative scheme by the viscosity approximation method for finding a common element of the set of solutions of the equilibrium problem and the set of fixed points of a finite family of nonexpansive mappings in a Hilbert space and we prove a strong convergence theorem in a Hilbert space which connected with Kangtunyakarn and Suantai [A. Kangtunyakarn and S. Suantai, Hybrid iterative scheme for generalized equilibrium problems and fixed point problems of finite family of nonexpansive mappings, Nonlinear Anal., 3 (2009), 296–309.] and Takahashi and Takahashi’s results [S. Takahashi andW. Takahashi, Viscosity approximation methods for equilibrium problems and fixed point problems in Hilbert spaces, J. Math. Anal. Appl., 331 (2007), 506– 515]. Our results extend and improve some recent corresponding results in the literature.