University of Isfahan Mathematics and Society 2345-6493 Articles in Press 2026 06 10 Ergodic theorems for a sequence of mappings in Banach spaces Ergodic theorems for a sequence of mappings in Banach spaces 30490 10.22108/msci.2026.148065.1786 FA Ali Yousefi Pirbasti Department of Mathematics, University of Zanjan, University blvd, Zanjan, Iran Hadi Khatibzadeh Department of Mathematics, University of Zanjan, University blvd, Zanjan, Iran Journal Article 2026 01 07 In this paper, ergodic convergence for a sequence of nonexpansive mappings in uniformly convex and uniformly smooth Banach spaces is studied. By introducing another definition of an almost orbit, an attempt is made to replace the uniform convergence condition with a weaker one. Our results provide a generalization of some classical ergodic convergence theorems for nonexpansive mappings. In this paper, ergodic convergence for a sequence of nonexpansive mappings in uniformly convex and uniformly smooth Banach spaces is studied. By introducing another definition of an almost orbit, an attempt is made to replace the uniform convergence condition with a weaker one. Our results provide a generalization of some classical ergodic convergence theorems for nonexpansive mappings. nonexpansive mapping ergodic theorem almost-orbit Fixed Point uniformly convex Banach space almost convergence https://math-sci.ui.ac.ir/article_30490_d1467f1a45beaa2a2c6d1a8c280cb172.pdf