On the shrinking projection method for nonexpansive mappings endowed with graphs
Abstract Recently, the convergence of a shrinking projection method for a Hadamard space satisfying some properties endowed with a directed graph defined on a nonempty closed convex subset of this space has been studied by many authors. In this work, we define a new graph and consider a Hadamard spa...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2025-06-01
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| Series: | Fixed Point Theory and Algorithms for Sciences and Engineering |
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| Online Access: | https://doi.org/10.1186/s13663-025-00791-8 |
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| _version_ | 1850102179511140352 |
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| author | Yasunori Kimura Supaluk Phothi Kittisak Tontan |
| author_facet | Yasunori Kimura Supaluk Phothi Kittisak Tontan |
| author_sort | Yasunori Kimura |
| collection | DOAJ |
| description | Abstract Recently, the convergence of a shrinking projection method for a Hadamard space satisfying some properties endowed with a directed graph defined on a nonempty closed convex subset of this space has been studied by many authors. In this work, we define a new graph and consider a Hadamard space endowed with our modified graph, we present a theorem on the strong convergence of an iterative sequence generated by the shrinking projection method. In particular, we generalize a result in (Khatoon et al. in Proc. Est. Acad. Sci 71(3):275, 2022) to more general setting. The similar result is also deduces to a Hilbert space. |
| format | Article |
| id | doaj-art-68f1f9bdccc84b3ab0c1ed52d06440f7 |
| institution | DOAJ |
| issn | 2730-5422 |
| language | English |
| publishDate | 2025-06-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Fixed Point Theory and Algorithms for Sciences and Engineering |
| spelling | doaj-art-68f1f9bdccc84b3ab0c1ed52d06440f72025-08-20T02:39:48ZengSpringerOpenFixed Point Theory and Algorithms for Sciences and Engineering2730-54222025-06-012025111210.1186/s13663-025-00791-8On the shrinking projection method for nonexpansive mappings endowed with graphsYasunori Kimura0Supaluk Phothi1Kittisak Tontan2Toho UniversityChiang Mai UniversityChiang Mai UniversityAbstract Recently, the convergence of a shrinking projection method for a Hadamard space satisfying some properties endowed with a directed graph defined on a nonempty closed convex subset of this space has been studied by many authors. In this work, we define a new graph and consider a Hadamard space endowed with our modified graph, we present a theorem on the strong convergence of an iterative sequence generated by the shrinking projection method. In particular, we generalize a result in (Khatoon et al. in Proc. Est. Acad. Sci 71(3):275, 2022) to more general setting. The similar result is also deduces to a Hilbert space.https://doi.org/10.1186/s13663-025-00791-8Shrinking projection methodG-nonexpansive mappingsDirected graphs |
| spellingShingle | Yasunori Kimura Supaluk Phothi Kittisak Tontan On the shrinking projection method for nonexpansive mappings endowed with graphs Fixed Point Theory and Algorithms for Sciences and Engineering Shrinking projection method G-nonexpansive mappings Directed graphs |
| title | On the shrinking projection method for nonexpansive mappings endowed with graphs |
| title_full | On the shrinking projection method for nonexpansive mappings endowed with graphs |
| title_fullStr | On the shrinking projection method for nonexpansive mappings endowed with graphs |
| title_full_unstemmed | On the shrinking projection method for nonexpansive mappings endowed with graphs |
| title_short | On the shrinking projection method for nonexpansive mappings endowed with graphs |
| title_sort | on the shrinking projection method for nonexpansive mappings endowed with graphs |
| topic | Shrinking projection method G-nonexpansive mappings Directed graphs |
| url | https://doi.org/10.1186/s13663-025-00791-8 |
| work_keys_str_mv | AT yasunorikimura ontheshrinkingprojectionmethodfornonexpansivemappingsendowedwithgraphs AT supalukphothi ontheshrinkingprojectionmethodfornonexpansivemappingsendowedwithgraphs AT kittisaktontan ontheshrinkingprojectionmethodfornonexpansivemappingsendowedwithgraphs |