Strong Convergence Theorems for Quasi-Bregman Nonexpansive Mappings in Reflexive Banach Spaces

Abstract EN

We study a strong convergence for a common fixed point of a finite family of quasi-Bregman nonexpansive mappings in the framework of real reflexive Banach spaces.

As a consequence, convergence for a common fixed point of a finite family of Bergman relatively nonexpansive mappings is discussed.

Furthermore, we apply our method to prove strong convergence theorems of iterative algorithms for finding a common solution of a finite family equilibrium problem and a common zero of a finite family of maximal monotone mappings.

Our theorems improve and unify most of the results that have been proved for this important class of nonlinear mappings.