On the convergence of modified Noor iterations with errors for asymptotically nonexpansive mappings. (English) Zbl 1097.47057

Summary: Several weak and strong convergence theorems are established for a modified Noor iterative scheme with errors for three asymptotically nonexpansive mappings in Banach spaces. Mann-type, Ishikawa-type, and Noor-type iterations are covered by the new iteration scheme. Our results extend and improve the recently announced ones [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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