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

被引：0

作者：

Termkaew, Sakan ^{[1
]}

Chaipunya, Parin ^{[1
,2
]}

Kohsaka, Fumiaki ^{[3
]}

机构：

[1] King Mongkuts Univ Technol Thonburi, Fac Sci, Dept Math, 126 Pracha Uthit Rd, Bangkok 10140, Thailand

[2] King Mongkuts Univ Technol Thonburi, Ctr Excellence Theoret & Computat Sci TaCS CoE, 126 Pracha Uthit Rd, Bangkok 10140, Thailand

[3] Tokai Univ, Fac Sci, Dept Math Sci, 4-1-1 Kitakaname, Hiratsuka, Kanagawa 2591292, Japan

来源：

OPEN MATHEMATICS | 2023年 / 21卷 / 01期

关键词：

convex optimization; ergodic theorem; fixed point; Hadamard space; nonexpansive mapping; WEAK-CONVERGENCE THEOREMS; CURVATURE; PROOF; SEMIGROUPS;

D O I：

10.1515/math-2023-0121

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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 non-expansive 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.

引用

页数：22

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