Strong convergence theorems for mixed equilibrium problems and Bregman relatively nonexpansive mappings in reflexive Banach spaces

Abstract

In this paper, we propose a new iterative method for solving the mixed equilibrium problems and the fixed point problems for a countable family of Bregman relatively nonexpansive mappings in reflexive Banach spaces. We prove that the sequence generated by the proposed iterative algorithm converges strongly to a common solution of the mentioned problems. Further, a numerical example of the iterative algorithm supporting our main result is presented.