On the shrinking projection method for nonexpansive mappings endowed with graphs

• Published in: Fixed 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
• Language: English
• 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
• ISSN: 2730-5422; 2730-5422
• DOI: 10.1186/s13663-025-00791-8

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.