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

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