Approximating fixed points of nonexpansive-type mappings in Hadamard spaces

Volume 39, Issue 4, pp 522--540 https://dx.doi.org/10.22436/jmcs.039.04.07

Publication Date: May 22, 2025 Submission Date: December 14, 2024 Revision Date: January 08, 2025 Accteptance Date: February 13, 2025

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Authors

W. Worapitpong - Departments of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thung Khru, Bangkok 10140, Thailand. P. Chaipunya - Departments of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thung Khru, Bangkok 10140, Thailand. - Center of Excellence in Theoretical and Computational Science (TaCS-CoE) & KMUTT Fixed Point Research Laboratory, Room SCL 802, Fixed Point Laboratory, Science Laboratory Building, Departments of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thung Khru, Bangkok 10140, Thailand. P. Kumam - Center of Excellence in Theoretical and Computational Science (TaCS-CoE) & KMUTT Fixed Point Research Laboratory, Room SCL 802, Fixed Point Laboratory, Science Laboratory Building, Departments of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thung Khru, Bangkok 10140, Thailand. S. Salisu - Center of Excellence in Theoretical and Computational Science (TaCS-CoE) & KMUTT Fixed Point Research Laboratory, Room SCL 802, Fixed Point Laboratory, Science Laboratory Building, Departments of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thung Khru, Bangkok 10140, Thailand. - Department of Mathematics, Faculty of Natural and Applied Sciences, Sule Lamido University Kafin Hausa, Jigawa, Nigeria.

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.

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Keywords

• Convergence analysis
• fixed point
• Hadamard space
• inverse strongly monotone
• nonexpansive mapping
• variational inequality
• viscosity iteration

MSC

•  47H09
•  47H10
•  47J05
•  47J25
•  49J40
•  53C23

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