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On the convergence of Mann and Ishikawa iterative processes for asymptotically \(\phi\)-strongly pseudocontractive mappings. (English) Zbl 1237.47076

Summary: We prove the equivalence and the strong convergence of (1) the modified Mann iterative process and (2) the modified Ishikawa iterative process for asymptotically \(\phi\)-strongly pseudocontractive mappings in a uniformly smooth Banach space.

MSC:

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