Approximating Common Fixed Points of Bregman Weakly Relatively Nonexpansive Mappings in Banach Spaces

Abstract EN

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 mapping T:C→C, where C is a closed and convex subset of a reflexive Banach space E.

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.