Convergence Theorems for Total Asymptotically Nonexpansive Mappings in CAT (0) Spaces

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Page Numbers: 291-309
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Published: May 17, 2026
Digital Object Identifier: 10.58578/ajstea.v4i3.9163
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Authors:
Ibrahim Usman Garba1*, M.I Bello2, M.S Adamu3, Pofi Ephraim4
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Ibrahim Usman Garba
Kurgwi Qua'an Pan L. G. C. Plateau State, Nigeria
M.I Bello
Kurgwi Qua'an Pan L. G. C. Plateau State, Nigeria
M.S Adamu
Kurgwi Qua'an Pan L. G. C. Plateau State, Nigeria
Pofi Ephraim
Kurgwi Qua'an Pan L. G. C. Plateau State, Nigeria

Abstract

This paper proposes new iterative algorithms for total asymptotically nonexpansive mappings in CAT(0) spaces. The study aims to establish a strong convergence theorem for the proposed algorithms under suitable mathematical conditions. Using a theoretical analytical approach, the convergence properties of the iterative schemes are examined within the geometric framework of CAT(0) spaces. The results demonstrate that the proposed algorithms converge strongly to a fixed point of total asymptotically nonexpansive mappings under the stated assumptions. These findings improve and extend several recent results reported in the literature on nonlinear mappings and fixed point theory. The study contributes to the advancement of convergence theory in CAT(0) spaces by providing refined iterative methods and strengthening the theoretical foundation for analyzing total asymptotically nonexpansive mappings.

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How to Cite
Garba, I. U., Bello, M., Adamu, M., & Ephraim, P. (2026). Convergence Theorems for Total Asymptotically Nonexpansive Mappings in CAT (0) Spaces. Asian Journal of Science, Technology, Engineering, and Art, 4(3), 291-309. https://doi.org/10.58578/ajstea.v4i3.9163

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Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.

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