Comparison of the Rate of Convergence among Picard, Mann, Ishikawa, and Noor Iterations Applied to Quasicontractive Maps

Comparison of the Rate of Convergence among Picard, Mann, Ishikawa, and Noor Iterations Applied to Quasicontractive Maps

<p/> <p>We provide sufficient conditions for Picard iteration to converge faster than Krasnoselskij, Mann, Ishikawa, or Noor iteration for quasicontractive operators. We also compare the rates of convergence between Krasnoselskij and Mann iterations for Zamfirescu operators.</p>

Bibliographic Details
Main Authors: Xue Zhiqun, Rhoades BE
Format: Article
Language:English
Published: SpringerOpen 2010-01-01
Series:Fixed Point Theory and Applications
Online Access:http://www.fixedpointtheoryandapplications.com/content/2010/169062
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spelling doaj-0c4e4bff9b304b57b450062c15aa3b552020-11-25T00:36:52ZengSpringerOpenFixed Point Theory and Applications1687-18201687-18122010-01-0120101169062Comparison of the Rate of Convergence among Picard, Mann, Ishikawa, and Noor Iterations Applied to Quasicontractive MapsXue ZhiqunRhoades BE<p/> <p>We provide sufficient conditions for Picard iteration to converge faster than Krasnoselskij, Mann, Ishikawa, or Noor iteration for quasicontractive operators. We also compare the rates of convergence between Krasnoselskij and Mann iterations for Zamfirescu operators.</p>http://www.fixedpointtheoryandapplications.com/content/2010/169062
collection DOAJ
language English
format Article
sources DOAJ
author Xue Zhiqun
Rhoades BE
spellingShingle Xue Zhiqun
Rhoades BE
Comparison of the Rate of Convergence among Picard, Mann, Ishikawa, and Noor Iterations Applied to Quasicontractive Maps
Fixed Point Theory and Applications
author_facet Xue Zhiqun
Rhoades BE
author_sort Xue Zhiqun
title Comparison of the Rate of Convergence among Picard, Mann, Ishikawa, and Noor Iterations Applied to Quasicontractive Maps
title_short Comparison of the Rate of Convergence among Picard, Mann, Ishikawa, and Noor Iterations Applied to Quasicontractive Maps
title_full Comparison of the Rate of Convergence among Picard, Mann, Ishikawa, and Noor Iterations Applied to Quasicontractive Maps
title_fullStr Comparison of the Rate of Convergence among Picard, Mann, Ishikawa, and Noor Iterations Applied to Quasicontractive Maps
title_full_unstemmed Comparison of the Rate of Convergence among Picard, Mann, Ishikawa, and Noor Iterations Applied to Quasicontractive Maps
title_sort comparison of the rate of convergence among picard, mann, ishikawa, and noor iterations applied to quasicontractive maps
publisher SpringerOpen
series Fixed Point Theory and Applications
issn 1687-1820
1687-1812
publishDate 2010-01-01
description <p/> <p>We provide sufficient conditions for Picard iteration to converge faster than Krasnoselskij, Mann, Ishikawa, or Noor iteration for quasicontractive operators. We also compare the rates of convergence between Krasnoselskij and Mann iterations for Zamfirescu operators.</p>
url http://www.fixedpointtheoryandapplications.com/content/2010/169062
work_keys_str_mv AT xuezhiqun comparisonoftherateofconvergenceamongpicardmannishikawaandnooriterationsappliedtoquasicontractivemaps
AT rhoadesbe comparisonoftherateofconvergenceamongpicardmannishikawaandnooriterationsappliedtoquasicontractivemaps
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