Convergence Comparison of Several Iteration Algorithms for the Common Fixed Point Problems

We discuss the following viscosity approximations with the weak contraction A for a non-expansive mapping sequence {Tn}, yn=αnAyn+(1−αn)Tnyn, xn+1=αnAxn+(1−αn)Tnxn. We prove that Browder's and Halpern's type convergenc...

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Autores principales:	Yisheng Song, Xiao Liu
Formato:	article
Lenguaje:	EN
Publicado:	SpringerOpen 2009
Materias:	Applied mathematics. Quantitative methods T57-57.97 Analysis QA299.6-433
Acceso en línea:	https://doaj.org/article/9ff0d5a4efd9490997d30ed0e4d118bd
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spelling	oai:doaj.org-article:9ff0d5a4efd9490997d30ed0e4d118bd2021-12-02T11:02:33ZConvergence Comparison of Several Iteration Algorithms for the Common Fixed Point Problems10.1155/2009/8243741687-18201687-1812https://doaj.org/article/9ff0d5a4efd9490997d30ed0e4d118bd2009-01-01T00:00:00Zhttp://dx.doi.org/10.1155/2009/824374https://doaj.org/toc/1687-1820https://doaj.org/toc/1687-1812We discuss the following viscosity approximations with the weak contraction A for a non-expansive mapping sequence {Tn}, yn=αnAyn+(1−αn)Tnyn, xn+1=αnAxn+(1−αn)Tnxn. We prove that Browder's and Halpern's type convergence theorems imply Moudafi's viscosity approximations with the weak contraction, and give the estimate of convergence rate between Halpern's type iteration and Mouda's viscosity approximations with the weak contraction. Yisheng SongXiao LiuSpringerOpenarticleApplied mathematics. Quantitative methodsT57-57.97AnalysisQA299.6-433ENFixed Point Theory and Applications, Vol 2009 (2009)
institution	DOAJ
collection	DOAJ
language	EN
topic	Applied mathematics. Quantitative methods T57-57.97 Analysis QA299.6-433
spellingShingle	Applied mathematics. Quantitative methods T57-57.97 Analysis QA299.6-433 Yisheng Song Xiao Liu Convergence Comparison of Several Iteration Algorithms for the Common Fixed Point Problems
description	We discuss the following viscosity approximations with the weak contraction A for a non-expansive mapping sequence {Tn}, yn=αnAyn+(1−αn)Tnyn, xn+1=αnAxn+(1−αn)Tnxn. We prove that Browder's and Halpern's type convergence theorems imply Moudafi's viscosity approximations with the weak contraction, and give the estimate of convergence rate between Halpern's type iteration and Mouda's viscosity approximations with the weak contraction.
format	article
author	Yisheng Song Xiao Liu
author_facet	Yisheng Song Xiao Liu
author_sort	Yisheng Song
title	Convergence Comparison of Several Iteration Algorithms for the Common Fixed Point Problems
title_short	Convergence Comparison of Several Iteration Algorithms for the Common Fixed Point Problems
title_full	Convergence Comparison of Several Iteration Algorithms for the Common Fixed Point Problems
title_fullStr	Convergence Comparison of Several Iteration Algorithms for the Common Fixed Point Problems
title_full_unstemmed	Convergence Comparison of Several Iteration Algorithms for the Common Fixed Point Problems
title_sort	convergence comparison of several iteration algorithms for the common fixed point problems
publisher	SpringerOpen
publishDate	2009
url	https://doaj.org/article/9ff0d5a4efd9490997d30ed0e4d118bd
work_keys_str_mv	AT yishengsong convergencecomparisonofseveraliterationalgorithmsforthecommonfixedpointproblems AT xiaoliu convergencecomparisonofseveraliterationalgorithmsforthecommonfixedpointproblems
_version_	1718396304389832704

Convergence Comparison of Several Iteration Algorithms for the Common Fixed Point Problems

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