Abstract
Using Bregman functions, we introduce a new hybrid iterative scheme for finding common fixed points of an infinite family of Bregman weakly relatively nonexpansive mappings in Banach spaces. We prove a strong convergence theorem for the sequence produced by the method. No closedness assumption is imposed on a mappingT:C→C, whereCis a closed and convex subset of a reflexive Banach spaceE. Furthermore, we apply our method to solve a system of equilibrium problems in reflexive Banach spaces. Some application of our results to the problem of finding a minimizer of a continuously Fréchet differentiable and convex function in a Banach space is presented. Our results improve and generalize many known results in the current literature.
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