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

Plubtieng, Somyot; Wangkeeree, Rabian; Punpaeng, Rattanaporn

J. Math. Anal. Appl. 322, No. 2, 1018-1029 (2006).

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.

MSC:

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

Keywords:

asymptotically nonexpansive mappings; uniform convexity; condition \((A^{\prime\prime})\); common fixed point; Opial condition; weak convergence; strong convergence

Citations:

Zbl 1011.47039; Zbl 1081.47063

References:

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