Strong convergence theorems for multi-step Noor iterations with errors in Banach spaces. (English) Zbl 1095.47042

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 B.–L. Xu and M. A. Noor [J. Math. Anal. Appl. 267, No. 2, 444–453 (2002; Zbl 1011.47039)], Y. J. Cho, H.–Y. Zhou and G.–T. Guo, Comput. Math. Appl. 47, No. 4–5, 707–717 (2004; Zbl 1081.47063)], and many others.


47J25 Iterative procedures involving nonlinear operators
47H09 Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc.
47H10 Fixed-point theorems
Full Text: DOI


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