The equivalence of Mann iteration and Ishikawa iteration for non-Lipschitzian operators
type: Item
instance of: scholarly article
title: The equivalence of Mann iteration and Ishikawa iteration for non-Lipschitzian operators
zbMATH Open document ID: 1045.47058
DOI: 10.1155/S0161171203211418
author: Ştefan M. Şoltuz
author: Billy E. Rhoades
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 2003-12-03T00:00:00Z
full work available at URL: https://eudml.org/doc/50914
review text: It is shown that the convergence of Mann iteration (one-step) is equivalent to the convergence of Ishikawa (two-step) iteration for various classes of non-Lipschitzian operators. Using essentially the technique of this paper, one can prove that the convergence of Mann-Ishikawa iteration is equivalent to the convergence of three-step iterations, which are known as Noor iteraions for non-Lipschitzian operators. Note that Noor iterations [introduced by \textit{M. Aslam Noor}, J. Math. Anal. Appl. 251, 217--229 (2000; Zbl 0964.49007)] include Mann-Ishikawa iterations as special cases.
reviewed by: Muhammad Aslam Noor
Mathematics Subject Classification ID: 47J25
Mathematics Subject Classification ID: 47H10
zbMATH DE Number: 2012566
zbMATH Keywords: Mann and Ishikawa iterations
zbMATH Keywords: non-Lipschitz operators
zbMATH Keywords: convergence
zbMATH Keywords: equivalence between one-step and two-step iterations
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description: scientific article; zbMATH DE number 2012566