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Convergence of three-step iterations scheme for nonself asymptotically nonexpansive mappings. (English) Zbl 1204.47087

Summary: Weak and strong convergence theorems of three-step iterations are established for nonself asymptotically nonexpansive mappings in uniformly convex Banach space. The results obtained in this paper extend and improve the recent ones announced by S.Suantai [J. Math.Anal.Appl.311, No.2, 506–517 (2005; Zbl 1086.47057)], S.H.Khan and N.Hussain [Comput.Math.Appl.55, No.11, 2544–2553 (2008; Zbl 1142.47335)], W.Nilsrakoo and S.Saejung [Appl.Math.Comput.181, No.2, 1026–1034 (2006; Zbl 1104.65053)], and many others.

MSC:

47J25 Iterative procedures involving nonlinear operators
47H09 Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc.
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References:

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