Iterative Method for a Generalized Equilibrium Problems and Fixed Point Problems of Nonexpansive Mappings in Hilbert spaces

In this paper, we introduce the iterative method for finding a com-mon element of the set of solutions of a generalized equilibrium prob-lem and the set of fixed points of a nonexpansive mapping in a Hilbert space and then obtain the sequence converges strongly to a common element of two sets. The results extended and improved the correspond-ing results of Plubtieng and Punpaeng [S. Plubtieng, R. Punpaeng, A new iterative method for equilibrium problems and fixed point prob-lems of nonexpansive mappings and monotone mappings, Appl. Math. Com. 197 (2008), 548-558.], Takahashi and Takahashi [ S. Takahashi, W. Takahashi, Strong convergence theorem for a generalized equilib-rium problem and nonexpansive mapping in a Hilbert space, Nonlinear Anal. 69(2008) 1025-1033.] and many others.