Strong convergence theorems for fixed point problems, variational inequality problems and system of generalized mixed equilibrium problems

The purpose of this paper is to construct a new iterative scheme by hybrid methods to approximate a common element of the common fixed points set of a finite family of ϕϕ-asymptotically nonexpansive mappings, the solutions set of a variational inequality problem and the solutions set of a system of generalized mixed equilibrium problems in a 2-uniformly convex real Banach space which is also uniformly smooth. Then, we prove strong convergence of the scheme to a common element of the three sets. Our results extend many known recent results in the literature.