Halpern's Iteration for Bregman Relatively Nonexpansive Mappings in Banach Spaces
Eskandar Naraghirad · Numerical Functional Analysis and Optimization · 2013
In this article, using Bregman functions, we first introduce new modified Mann and Halpern's iterations for finding common fixed points of an infinite family of Bregman relatively nonexpansive mappings in the framework of Banach spaces. Furthermore, we prove the strong convergence theorems for the sequences produced by the methods. Finally, we apply these results for approximating zeroes of accretive operators. Our results improve and generalize many known results in the current literature.