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On Noor iterations for asymptotically nonexpansive mappings in Banach spaces. (English) Zbl 1170.47053

Summary: In a real Banach space, we consider the problem of the convergence of the Noor iterative sequences for asymptotically nonexpansive mappings. Under suitable conditions, it is proved that the iterative sequence converges strongly to a fixed point which is also a solution of a certain variation inequality. The results presented in this paper extend and improve some recent results.

MSC:

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