## Behzad Djafari Rouhani, Hadi Khatibzadeh, Vahid Mohebbi, Ergodic and fixed point theorems for Bregman nonexpansive sequences and mappings in Banach spaces

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DOI: 10.23952/asvao.4.2022.3.05
Volume 4, Issue 3, 1 December 2022, Pages 311-321

Abstract. 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 $\phi$-nonexpansive sequences and give a partial answer to the open problem raised in 1981 by Djafari Rouhani for nonexpansive sequences in a Banach space.