A Dual Ergodic Theorem in Banach Spaces

Document Type : Original Article

Authors
Ali Yousefi Pirbasti 1 ΒΆ
Hadi Khatibzadeh 2
1 Department of Math., University of Zanjan
2 Department of Mathematics, University of Zanjan, University blvd., Iran.
10.22034/maco.5.2.11
Abstract
In uniformly smooth Banach spaces, we prove a dual ergodic theorem for an almost-orbit of a sequence of nonexpansive mappings. We also present a new definition of almost-orbit for a sequence of nonexpansive mappings and prove the dual ergodic theorem for this sequence. This results extend the dual ergodic theorem established by Bruck and Reich for iterations of nonexpansive mappings as well as ergodic theorems for a sequence of nonexpansive mappings from Hilbert spaces to Banach spaces. Finally, some applications to fixed point iterative methods for nonexpansive mappings and the proximal point algorithm for m-accretive operators to approximate a zero of the operator are presented.

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2025.
Mathematical Analysis and Convex Optimization
Volume 5, Issue 2
December 2025