Mean ergodic theorems for a sequence of nonexpansive mappings in complete CAT(0) spaces and its applications

Journal article

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Publication Details

Author list: Termkaew, Sakan; Chaipunya, Parin; Kohsaka, Fumiaki

Publisher: De Gruyter

Publication year: 2023

Volume number: 21

Issue number: 1

eISSN: 2391-5455

URL: https://www.scopus.com/inward/record.uri?eid=2-s2.0-85173721805&doi=10.1515%2fmath-2023-0121&partnerID=40&md5=bd4ed9359581fadc4c5b768945366710

Languages: English-Great Britain (EN-GB)

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Abstract

In this article, we prove ergodic convergence for a sequence of nonexpansive mappings in Hadamard (complete CAT (0)) spaces. Our result extends the nonlinear ergodic theorem by Baillon for nonexpansive mappings from Hilbert spaces to Hadamard spaces. We further establish the standard nonlinear ergodic theorem and apply our results to the problem of finding a common fixed point of a countable family of nonexpansive mappings. Finally, we propose some applications of our results to solve convex optimization problems in Hadamard spaces. ฉ 2023 the author(s), published by De Gruyter.

Keywords

ergodic theorem