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<p>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, <CitationRef CitationID="CR6">2022</CitationRef>) to more general setting. The similar result is also deduces to a Hilbert space.</p>

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On the shrinking projection method for nonexpansive mappings endowed with graphs

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年6月9日

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  • Yasunori Kimura,
  • Supaluk Phothi,
  • Kittisak Tontan

摘要

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.