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Zbl 1095.47042
Plubtieng, Somyot; Wangkeeree, Rabian
Strong convergence theorems for multi-step Noor iterations with errors in Banach spaces. (English)
[J] J. Math. Anal. Appl. 321, No. 1, 10-23 (2006). ISSN 0022-247X

Summary: We establish two strong convergence theorems for a multi-step Noor iterative scheme with errors for mappings which are asymptotically nonexpansive in the intermediate sense (or asymptotically quasi-nonexpansive, respectively) in Banach spaces. Our results extend and improve recent ones announced by {\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.

MSC 2000:: *47J25 Methods for solving nonlinear operator equations (general)
47H09 Mappings defined by "shrinking" properties
47H10 Fixed point theorems for nonlinear operators on topol.linear spaces

Keywords: asymptotically nonexpansive in the intermediate sense; asymptotically quasi-nonexpansive mappings; completely continuous; uniformly convex; uniformly $L$-Lipschitzian

Citations: Zbl 1011.47039; Zbl 1081.47063

Cited in: Zbl 1178.47044 Zbl 1150.47354 Zbl 1183.47072

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