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On \(\Delta\)-convergence theorems in CAT\((0)\) spaces. (English) Zbl 1165.65351
Summary: By using the concept of \(\Delta\)-convergence introduced by T.-C. Lim [Proc. Am. Math. Soc. 60, 179–182 (1976; Zbl 0346.47046)], we are able to give the CAT\((0)\) space analogs of results on weak convergence of the Picard, Mann and Ishikawa iterates proved in uniformly convex Banach spaces by Z. Opial [Bull. Am. Math. Soc. 73, 591–597 (1967; Zbl 0179.19902)], S. Ishikawa [Proc. Am. Math. Soc. 59, 65–71 (1976; Zbl 0352.47024)] and K. K. Tan and H. K. Xu [J. Math. Anal. Appl. 178, 301–308 (1993; Zbl 0895.47048)].

MSC:
65J15 Numerical solutions to equations with nonlinear operators
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