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Weak and strong convergence theorems for three-step iterations with errors for asymptotically nonexpansive mappings. (English) Zbl 1081.47063
In the present paper, several weak and strong convergence theorems are established for three-step iterative schemes with errors for asymptotically nonexpansive mappings. The results presented extend and improve the recent ones announced by K.–K. Tan and H. K. Xu [Proc. Am. Math. Soc. 122, No. 3, 733–739 (1994; Zbl 0820.47071)], B.–L. Xu and M. A. Noor [J. Math. Anal. Appl. 267, No. 2, 444–453 (2002; Zbl 1011.47039)], and others.

MSC:
47J25 Iterative procedures involving nonlinear operators
47H09 Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc.
65J15 Numerical solutions to equations with nonlinear operators (do not use 65Hxx)
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