Iterative Solution of Fixed Points Problem, System of Generalized Mixed Equilibrium Problems and Variational Inclusion Problems

In this paper, we study an algorithm for finding a common element of the set of common fixed points of an infinite family of asymptotically nonexpansive mappings, the set of common solutions to a system of generalized mixed equilibrium problems and the set of solutions to variational inclusion in a real Hilbert space. We prove that the scheme converges strongly to a common element of the three afore mentioned sets. Finally, we give applications of our results to Optimization problems in a real Hilbert space.