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: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2025-06-01
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| 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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| Summary: | 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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| ISSN: | 2730-5422 |