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Xu, Benlong; Aslam Noor, Muhammad

Fixed-point iterations for asymptotically nonexpansive mappings in Banach spaces. (English) Zbl 1011.47039

J. Math. Anal. Appl. 267, No. 2, 444-453 (2002).
The authors suggest a new class of three step iterative schemes for solving nonlinear equations \(Tx=x\) with asymptotically nonexpansive mappings in Banach spaces. The Ishikawa-type and Mann-type iteration schemes are included as particular cases. The convergence of the new schemes is proved.
Reviewer: Milan Kučera (Praha)

Cited in 37 Reviews
Cited in 85 Documents

MSC:

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

Keywords:

three step iterations; asymptotically nonexpansive mappings; uniformly convex Banach spaces; Mann-type and Ishikawa-type iterations
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References:

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