Inertial Iterative Method for Generalized Mixed Equilibrium Problem and Fixed Point Problem

Abstract

In this paper, we study the generalized mixed equilibrium problem and the fixed point problem. We propose an inertial iterative method for approximating the common solution of a generalized mixed equilibrium problem of a monotone mapping and a fixed point problem for a Bregman strongly nonexpansive mapping in the framework of real reflexive Banach spaces. Under certain mild conditions, we obtain a strong convergence result of the proposed method. Finally, we present numerical examples to illustrate the applicability of our method.