## 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.

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, 35, 171-174, (1972) · Zbl 0256.47045 [2] Plubtieng, S; Wangkeeree, R, Strong convergence theorems for multi-step Noor iterations with errors in Banach spaces, Journal of Mathematical Analysis and Applications, 321, 10-23, (2006) · Zbl 1095.47042 [3] Liu, Q, Iterative sequences for asymptotically quasi-nonexpansive mappings with error member, Journal of Mathematical Analysis and Applications, 259, 18-24, (2001) · Zbl 1001.47034 [4] Schu, J, Iterative construction of fixed points of strictly pseudocontractive mappings, Applicable Analysis, 40, 67-72, (1991) · Zbl 0697.47061
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