On generalized Bregman nonspreading mappings and zero points of maximal monotone operator in a reflexive Banach space

Abstract

The purpose of this paper is to investigate the existence and approximation of fixed points of generalized Bregman nonspreading mapping which are also the zero points of maximal monotone operator in a real reflexive Banach space. Without assuming the ‘AKTT’ condition, we prove a strong convergence theorem for approximating a common element in the set of fixed points of system of generalized Bregman nonspreading mappings and the set of zero points of system of maximal monotone operators in a real reflexive Banach space. Our results improve and generalized many recent results in the literature.