Common solution of generalized mixed equilibrium problem and bregman strongly nonexpansive mapping in reflexive banach spaces

Abstract

This paper introduces an iterative algorithm for approximating a common solution of generalized mixed equilibrium problem and fixed point problem in a real reflexive Banach space. Using this new algorithm, a strong convergence theorem is proved concerning an element in the intersection of set of solutions of generalized mixed equilibrium problem and the set of solutions of fixed point for a finite family of Bregman strongly nonexpansive mappings. The method of proof in this work is innovative and of independent interest.