A new iterative method for solving a system of generalized equilibrium problems, generalized mixed equilibrium problems and common fixed point problems in Hilbert spaces

Abstract

In this paper, we introduce an 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.