Mean ergodic theorems for a sequence of nonexpansive mappings in complete CAT(0) spaces and its applications
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 standar...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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De Gruyter
2023-10-01
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| Series: | Open Mathematics |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/math-2023-0121 |
| _version_ | 1827794726707789824 |
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| author | Termkaew Sakan Chaipunya Parin Kohsaka Fumiaki |
| author_facet | Termkaew Sakan Chaipunya Parin Kohsaka Fumiaki |
| author_sort | Termkaew Sakan |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-11T18:38:56Z |
| format | Article |
| id | doaj.art-93ad94dc39ab4aac851b7e3c8bce6600 |
| institution | Directory Open Access Journal |
| issn | 2391-5455 |
| language | English |
| last_indexed | 2024-03-11T18:38:56Z |
| publishDate | 2023-10-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Open Mathematics |
| spelling | doaj.art-93ad94dc39ab4aac851b7e3c8bce66002023-10-12T14:06:59ZengDe GruyterOpen Mathematics2391-54552023-10-01211708210.1515/math-2023-0121Mean ergodic theorems for a sequence of nonexpansive mappings in complete CAT(0) spaces and its applicationsTermkaew Sakan0Chaipunya Parin1Kohsaka Fumiaki2Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi, 126 Pracha Uthit Rd., Bang Mod, Thung Khru, Bangkok, 10140, ThailandDepartment of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi, 126 Pracha Uthit Rd., Bang Mod, Thung Khru, Bangkok, 10140, ThailandDepartment of Mathematical Sciences, Faculty of Science, Tokai University, 4-1-1 Kitakaname, Hiratsuka, Kanagawa, 259-1292, JapanIn 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.https://doi.org/10.1515/math-2023-0121convex optimizationergodic theoremfixed pointhadamard spacenonexpansive mapping47h0947h1047h2547n10 |
| spellingShingle | Termkaew Sakan Chaipunya Parin Kohsaka Fumiaki Mean ergodic theorems for a sequence of nonexpansive mappings in complete CAT(0) spaces and its applications Open Mathematics convex optimization ergodic theorem fixed point hadamard space nonexpansive mapping 47h09 47h10 47h25 47n10 |
| title | Mean ergodic theorems for a sequence of nonexpansive mappings in complete CAT(0) spaces and its applications |
| title_full | Mean ergodic theorems for a sequence of nonexpansive mappings in complete CAT(0) spaces and its applications |
| title_fullStr | Mean ergodic theorems for a sequence of nonexpansive mappings in complete CAT(0) spaces and its applications |
| title_full_unstemmed | Mean ergodic theorems for a sequence of nonexpansive mappings in complete CAT(0) spaces and its applications |
| title_short | Mean ergodic theorems for a sequence of nonexpansive mappings in complete CAT(0) spaces and its applications |
| title_sort | mean ergodic theorems for a sequence of nonexpansive mappings in complete cat 0 spaces and its applications |
| topic | convex optimization ergodic theorem fixed point hadamard space nonexpansive mapping 47h09 47h10 47h25 47n10 |
| url | https://doi.org/10.1515/math-2023-0121 |
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