Convergence Theorems for Total Asymptotically Nonexpansive Mappings in CAT (0) Spaces - Ibrahim Usman Garba; M.I Bello; M.S Adamu; Pofi Ephraim (Asian Journal of Science, Technology, Engineering, and Art, 2026)
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.