An inertial method for solving systems of generalized mixed equilibrium and fixed point problems in reflexive Banach spaces

Abstract

The Generalized mixed equilibrium problems, which includes the equilibrium and mixed equilibrium problem of monotone type mapping is considered in this paper with the fixed point of Bregman strongly nonexpansive mapping in the framework of real reflexive Banach space. We approximate the common solution of the system of generalized mixed equilibrium and fixed point problems for the finite family of Bregman strongly nonexpansive mappings using an inertial Halpern method. Using our iterative method, we prove a strong convergence result for solving the aforementioned problems. We also present some applications and numerical examples to demonstrate the performance of our iterative method. Our result improves and extends some important results presented by authors in the literature.