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Modified Ishikawa iteration process with errors in Banach spaces. (English) Zbl 1237.47078

Summary: The purpose of this paper is to investigate the problem of approximating the fixed points of uniformly Lipschitzian asymptotically pseudocontractive mappings in an arbitrary real Banach space by modified Ishikawa iterative sequences with errors. Removing the restriction \(\lim_{n \to \infty}\beta _{n} = 0\), we prove that S.-S. Zhang’s results [Acta Math. Appl. Sin. 24, No. 2, 236–241 (2001; Zbl 1020.47064)] remain true. On the other hand, we also extend his results to the case of the modified Ishikawa iterative sequences with errors.

MSC:

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

Citations:

Zbl 1020.47064
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