Approximation of common solution of a system of equilibrium problem and fixed point of generalized Bregman nonspreading mappings in Banach spaces

Abstract

In this paper, we introduce a hybrid iterative method for approximating the common solution of a systems of generalized mixed equilibrium problem and the class of [Formula: see text]-generalized Bregman nonspreading mappings in reflexive Banach space. We prove the asymptotic fixed point property of the class of [Formula: see text]-generalized Bregman nonspreading mappings in reflexive Banach spaces and provide a strong convergence theorem for solving the problem under some mild conditions. Furthermore, some numerical results were presented to show the important and computational performance of the proposed method. This result extends and generalized many interesting results in the contemporary literature.