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Strong convergence of a general iteration scheme in \(CAT(0)\) spaces. (English) Zbl 1202.47076
Summary: We introduce and study strong convergence of a general iteration scheme for a finite family of asymptotically quasi-nonexpansive maps in convex metric spaces and \(CAT(0)\) spaces. The new iteration scheme includes modified Mann and Ishikawa iterations, the three-step iteration scheme of B.-L. Xu and M. A. Noor [J. Math. Anal. Appl. 267, No. 2, 444–453 (2002; Zbl 1011.47039)] and the scheme of A. R. Khan, A. A. Domlo and H. Fukhar-Ud-Din [J. Math. Anal. Appl. 341, No. 1, 1–11 (2008; Zbl 1137.47053)] as special cases in Banach spaces. Our results are refinements and generalizations of several recent results from the current literature.

MSC:
47J25 Iterative procedures involving nonlinear operators
54H25 Fixed-point and coincidence theorems (topological aspects)
47H09 Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc.
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