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On the convergence of modified Noor iterations with errors for asymptotically nonexpansive mappings. (English) Zbl 1097.47057
Summary: Several weak and strong convergence theorems are established for a modified Noor iterative scheme with errors for three asymptotically nonexpansive mappings in Banach spaces. Mann-type, Ishikawa-type, and Noor-type iterations are covered by the new iteration scheme. Our results extend and improve the recently announced ones [{\it B.--L. Xu} and {\it M. A. Noor}, J. Math. Anal. Appl. 267, No. 2, 444--453 (2002; Zbl 1011.47039); {\it Y. J. Cho, H.--Y. Zhou} and {\it G.--T. Guo}, Comput. Math. Appl. 47, No. 4--5, 707--717 (2004; Zbl 1081.47063)], and many others.

47J25Iterative procedures (nonlinear operator equations)
47H09Mappings defined by “shrinking” properties
47H10Fixed-point theorems for nonlinear operators on topological linear spaces
Full Text: DOI
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