完备CAT(0)空间中非扩张映射序列的平均遍历定理及其应用

IF 0.9 4区数学 Q1 MATHEMATICS

Open Mathematics Pub Date : 2023-01-01 DOI:10.1515/math-2023-0121

Sakan Termkaew, Parin Chaipunya, Fumiaki Kohsaka

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引用次数: 0

摘要

摘要本文证明了Hadamard(完全CAT (0) {\rm{CAT}}\left(0))空间中一个非扩张映射序列的遍历收敛性。我们的结果推广了Hilbert空间到Hadamard空间非扩张映射的非线性遍历定理。进一步建立了标准非线性遍历定理，并将结果应用于求可数非扩张映射族的公共不动点问题。最后，我们给出了我们的结果在求解Hadamard空间中的凸优化问题中的一些应用。

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

Abstract In this article, we prove ergodic convergence for a sequence of nonexpansive mappings in Hadamard (complete CAT ( 0 ) {\rm{CAT}}\left(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.

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来源期刊

Open Mathematics MATHEMATICS-

CiteScore

2.40

自引率

5.90%

发文量

审稿时长

16 weeks

期刊介绍： Open Mathematics - formerly Central European Journal of Mathematics Open Mathematics is a fully peer-reviewed, open access, electronic journal that publishes significant, original and relevant works in all areas of mathematics. The journal provides the readers with free, instant, and permanent access to all content worldwide; and the authors with extensive promotion of published articles, long-time preservation, language-correction services, no space constraints and immediate publication. Open Mathematics is listed in Thomson Reuters - Current Contents/Physical, Chemical and Earth Sciences. Our standard policy requires each paper to be reviewed by at least two Referees and the peer-review process is single-blind. Aims and Scope The journal aims at presenting high-impact and relevant research on topics across the full span of mathematics. Coverage includes: