Hybrid Iterative Method for Solving a System of Generalized Equilibrium Problems, Generalized Mixed Equilibrium Problems and Common Fixed Point Problems in Hilbert Spaces

Benjawan Rodjanadid

Abstract

In this paper, we propose a hybrid iterative method for finding a common element of the set of solutions of a generalized mixed equilibrium problem (GMEP), the solutions of a general system of equilibrium problem and the set of common fixed points of a finite family of nonexpansive mappings in a real Hilbert space. Then, we prove that the sequence converges strongly to a common element of the above three sets. Furthermore, we apply our result to prove four new strong convergence theorems in fixed point problems, mixed equilibrium problems,  generalized equilibrium problems , equilibrium problems and variational inequality.