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Strong convergence theorems for common fixed points of multistep iterations with errors in Banach spaces. (English) Zbl 1178.47044

Summary: We establish a strong convergence theorem for a multi-step iterative scheme with errors for asymptotically nonexpansive mappings in the intermediate sense in Banach spaces. Our results extend and improve the recent ones announced by S.Plubtieng and R.Wangkeeree [J. Math.Anal.Appl.321, No.1, 10–23 (2006; Zbl 1095.47042)] and many others.

MSC:

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

Citations:

Zbl 1095.47042
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References:

[1] Goebel K, Kirk WA: A fixed point theorem for asymptotically nonexpansive mappings.Proceedings of the American Mathematical Society 1972,35(1):171-174. 10.1090/S0002-9939-1972-0298500-3 · Zbl 0256.47045 · doi:10.1090/S0002-9939-1972-0298500-3
[2] Plubtieng S, Wangkeeree R: Strong convergence theorems for multi-step Noor iterations with errors in Banach spaces.Journal of Mathematical Analysis and Applications 2006,321(1):10-23. 10.1016/j.jmaa.2005.08.029 · Zbl 1095.47042 · doi:10.1016/j.jmaa.2005.08.029
[3] Liu Q: Iterative sequences for asymptotically quasi-nonexpansive mappings with error member.Journal of Mathematical Analysis and Applications 2001,259(1):18-24. 10.1006/jmaa.2000.7353 · Zbl 1001.47034 · doi:10.1006/jmaa.2000.7353
[4] Schu J: Iterative construction of fixed points of strictly pseudocontractive mappings.Applicable Analysis 1991,40(2-3):67-72. 10.1080/00036819108839994 · Zbl 0697.47061 · doi:10.1080/00036819108839994
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