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Convergence criteria of modified Noor iterations with errors for asymptotically nonexpansive mappings. (English) Zbl 1087.47054
Over the past years, several researchers have spent a lot of effort to create new iteration schemes to approximate a fixed point of a suitable selfmap of a Banach space with some specific properties. In the paper under review, the authors start from the Noor [{\it B. Xu} and {\it M. A. Noor}, J. Math. Anal. Appl. 267, No. 2, 444--453 (2002; Zbl 1011.47039)] and modified Noor [{\it S. Suantei}, ibid. 311, No. 2, 506--517 (2005; Zbl 1086.47057)] three-step iterative scheme, and turn it into a modified Noor iteration scheme with errors. They prove then both strong and weak convergence theorems for an asymptotically nonexpansive (when needed, also supposed to be completely continuous) mapping in a uniformly convex Banach space (when needed, also supposed to satisfy Opial’s condition).

MSC:
47J25Iterative procedures (nonlinear operator equations)
47H09Mappings defined by “shrinking” properties
WorldCat.org
Full Text: DOI
References:
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