An inertial iterative method for split generalized vector mixed equilibrium and fixed point problems.

Abstract

In this paper, we introduce an inertial-type algorithm for approximating a common solution of split generalized mixed vector equilibrium and fixed point problems. In the framework of real Hilbert spaces, we state and prove a strong convergence theorem for obtaining a common solution of split generalized mixed vector equilibrium problem and fixed point of a finite family of nonexpansive mappings. Furthermore, we give some consequences of our main result and also report some numerical illustrations to display the performance of our method. The result obtained in this paper unifies and generalizes other corresponding results in the literature