On the shrinking projection method for nonexpansive mappings endowed with graphs

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 endowe...

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Published inFixed point theory and algorithms for sciences and engineering Vol. 2025; no. 1; pp. 9 - 12
Main Authors Kimura, Yasunori, Phothi, Supaluk, Tontan, Kittisak
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.12.2025
Springer Nature B.V
SpringerOpen
Subjects
Algorithms
Analysis
Applications of Mathematics
Approximation
Convergence
Differential Geometry
Directed graphs
G-nonexpansive mappings
Graph theory
Graphs
Hilbert space
Iterative methods
Mathematical and Computational Biology
Mathematics
Mathematics and Statistics
Methods
Shrinking projection method
Topology
Shrinking projection method
47H09
47H10
Directed graphs
nonexpansive mappings
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Summary: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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ISSN:2730-5422
2730-5422
DOI:10.1186/s13663-025-00791-8