The equivalence between the convergence of modified Picard, modified Mann, and modified Ishikawa iterations
type: Item
instance of: scholarly article
title: The equivalence between the convergence of modified Picard, modified Mann, and modified Ishikawa iterations
zbMATH Open document ID: 1065.47054
DOI: 10.1016/S0895-7177(03)00113-4
author: Shihsen Chang
author: Yeol Je Cho
author: J. K. Kim
published in: Mathematical and Computer Modelling
publication date: 2004-08-06T00:00:00Z
review text: The authors consider equivalence between the convergence for the modified Picard iteration, the modified Mann iteration, and the modified Ishikawa iteration. All those modified iterations are for \(L\)-Lipschitz mappings, Banach contractive mappings, nonexpansive mappings, and asymptotically nonexpansive mappings in Banach spaces. Some conditions related to positive series are proved to be sufficient for the mentioned equivalence.
reviewed by: Zhilin Yang
Mathematics Subject Classification ID: 47H10
Mathematics Subject Classification ID: 47J25
Mathematics Subject Classification ID: 65J15
Mathematics Subject Classification ID: 47H09
zbMATH DE Number: 2082773
zbMATH Keywords: uniformly \(L\)-Lipschitzian mapping
zbMATH Keywords: asymptotically non-expansive mapping
zbMATH Keywords: non-expansive mapping
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 2082773