Mann and Ishikawa iterations with errors for asymptotically nonexpansive mappings

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Abstract

In a recent paper, Rhoades [1] presented some generalizations of Schu [2] on the convergence of the Mann and Ishikawa iterations of asymptotically nonexpansive mappings in uniformly convex Banach spaces. We continue the study on the Ishikawa (and Mann) iteration process with errors and prove that if X is a uniformly convex Banach space, øEX closed bounded and convex, and T : EE is an asymptotically nonexpansive mapping, then the Ishikawa (and Mann) iteration process with errors converges strongly to some fixed point of T.

Keywords

Ishikawa iteration process with errors
Asymptotically nonexpansive mappings
Uniformly convex spaces

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1

The author wishes to thank the referees for their valuable suggestions. The author is supported by the National Natural Science Foundation of P.R. China (special program for outstanding young researchers) under Grant No. 19801017.