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

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.