Hybrid iterative algorithm for an infinite families of closed, uniformly asymptotic regular and uniformly Bregman totally quasi-D-asymptotically nonexpansive mappings in Banach spaces

A new hybrid Bregman projection method is considered for finding common solutions of the set of common fixed points of an infinite family of closed, uniformly asymptotic regular and uniformly Bregman totally quasi-D-asymptotically nonexpansive mappings, the set of solutions to a variational inequality problem and the set of common solutions to a system of generalized mixed equilibrium problems, strong convergence theo- rems of common elements are proved by using new analysis techniques and Bregman mappings in the setting of uniformly smooth and 2-uniformly convex real Banach spaces. Our results improve and generalize many important known recent results in the current literature, because Bregman projection mapping generalizes the generalized projection mapping and the metric projection mapping.