Weak Convergence Theorems for Bregman Relatively Nonexpansive Mappings in Banach Spaces - Chin-Tzong Pang; Eskandar Naraghirad; Ching-Feng Wen (Journal of Applied Mathematics)
We study Mann type iterative algorithms for finding fixed points of Bregman relatively nonexpansive mappings in Banach spaces. By exhibiting an example, we first show that the class of Bregman relatively nonexpansive mappings embraces properly the class of Bregman strongly nonexpansive mappings which was investigated by Martín-Márques et al. (2013). We then prove weak convergence theorems for the sequences produced by the methods. Some application of our results to the problem of finding a zero of a maximal monotone operator in a Banach space is presented. Our results improve and generalize many known results in the current literature.