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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Main Authors: Yasunori Kimura, Supaluk Phothi, Kittisak Tontan
Format: Article
Language:English
Published: SpringerOpen 2025-06-01
Series:Fixed Point Theory and Algorithms for Sciences and Engineering
Subjects:
Online Access:https://doi.org/10.1186/s13663-025-00791-8
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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.
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id doaj-art-68f1f9bdccc84b3ab0c1ed52d06440f7
institution DOAJ
issn 2730-5422
language English
publishDate 2025-06-01
publisher SpringerOpen
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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