Approximating fixed points of nonexpansive-type mappings in Hadamard spaces

Journal article

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Strategic Research Themes

Modeling Design and Optimization (Computational Science and Engineering)

Publication Details

Author list: Worapitpong W.; Chaipunya P.; Kumam P.; Salisu S.

Publication year: 2025

Journal: Journal of Mathematics and Computer Science (2008-949X)

Volume number: 39

Issue number: 4

Start page: 522

End page: 540

Number of pages: 19

ISSN: 2008-949X

URL: https://www.scopus.com/inward/record.uri?eid=2-s2.0-105007177007&doi=10.22436%2fjmcs.039.04.07&partnerID=40&md5=e0f07044a94221d2b880d2839169b655

Languages: English-Great Britain (EN-GB)

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Abstract

Certain essential properties of a generalized nonexpansive mapping, showcasing an inclusion relation to known mappings within the framework of Hadamard spaces, are investigated in this work. Additionally, a viscosity-type algorithm is proposed for approximating fixed points of such mappings. The strong convergence of the sequences generated by this algorithm is demonstrated under appropriate assumptions. As an application of the findings, the existence of a solution to the variational inequality problem involving the mapping is established. Furthermore, an iterative scheme is derived, exhibiting strong convergence towards solving the variational inequality problem. To demonstrate the implementation of the proposed algorithm, a numerical example is provided in a non-Hilbert CAT(0) space. © 2025 All rights reserved.

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