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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:
47H09Mappings defined by “shrinking” properties
47H10Fixed-point theorems for nonlinear operators on topological linear spaces
47J25Iterative procedures (nonlinear operator equations)
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References:
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