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Strong convergence theorems of nonself asymptotically nonexpansive mapping in Banach spaces. (English) Zbl 1221.47134

Summary: We obtain the strong convergence of a Halpern type iterative scheme to a fixed point of a non-self asymptotically nonexpansive mapping with respect to a retraction \(P\) in Banach spaces. Our results improve and extend the corresponding results of Jung [6], Song [12,13], and Aoyama [2].

MSC:

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