On the equivalence of the convergence criteria between modified Mann-Ishikawa and multi-step iterations with errors for successively strongly pseudo-contractive operators
type: Item
instance of: scholarly article
title: On the equivalence of the convergence criteria between modified Mann-Ishikawa and multi-step iterations with errors for successively strongly pseudo-contractive operators
zbMATH Open document ID: 1106.65050
author: Fanwei Bu
author: Zhenyu Huang
author: Muhammad Aslam Noor
published in: Applied Mathematics and Computation
publication date: 2006-10-31T00:00:00Z
review text: The authors prove the equivalence of the convergence between the modified Mann- Ishikawa and multi-step Noor iterations with errors for the successively strongly pseudo-contractive operators without Lipschitzian assumption. By extending to the more generalized multi-step iterations with errors, the results obtained in this paper generalize the results of \textit{B. E. Rhoades} and \textit{S. M. Soltuz} [Nonlinear Anal., Theory Methods Appl. 58A, No. 1--2, 219--228 (2004; Zbl 1064.47070); J. Math. Anal. Appl. 289, 266--278 (2004; Zbl 1053.47055)]. On the other hand, by providing the equivalence of convergence between all of these up-to-date iteration schemes, these results improve the corresponding results of all references in the bibliography.
reviewed by: Yuxia Guo
Mathematics Subject Classification ID: 65J15
Mathematics Subject Classification ID: 47J25
Mathematics Subject Classification ID: 47H09
zbMATH DE Number: 5069180
zbMATH Keywords: Mann-Ishikawa iteration
zbMATH Keywords: multi-step Noar iteration
MaRDI profile type: Publication
full work available at URL: j.amc.2005.12.041
OpenAlex ID: W2001834009
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DOI: 10.1016/J.AMC.2005.12.041
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description: scientific article; zbMATH DE number 5069180