ERGODIC AND FIXED POINT THEOREMS FOR BREGMAN NONEXPANSIVE SEQUENCES AND MAPPINGS IN BANACH SPACES

In this paper, we introduce the notion of Bregman nonexpansive sequences and mappings in a Banach space, prove an ergodic theorem and a fixed point theorem, and some weak convergence theorems for such sequences and maps with rather mild assumptions on the Banach space. These results extend our previous results for φ-nonexpansive sequences and give a partial answer to the open problem raised in 1981 by Djafari Rouhani for nonexpansive sequences in a Banach space. ©2022 Applied Set-Valued Analysis and Optimization.