Viscosity Approximation Methods for Generalized Equilibrium Problems and Fixed Point Problems of Finite Family of Nonexpansive Mappings in Hilbert Spaces

Utith Inprasit

Abstract

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.