An Extragradient Method and Proximal Point Algorithm for Inverse Strongly Monotone Operators and Maximal Monotone Operators in Banach Spaces

<p>Abstract</p> <p>We introduce an iterative scheme for finding a common element of the solution set of a maximal monotone operator and the solution set of the variational inequality problem for an inverse strongly-monotone operator in a uniformly smooth and uniformly convex Banach...

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Autores principales:	Plubtieng Somyot, Sriprad Wanna
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/5dde2ad233ac4e6d86fc75410ea8cd11
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spelling	oai:doaj.org-article:5dde2ad233ac4e6d86fc75410ea8cd112021-12-02T12:06:21ZAn Extragradient Method and Proximal Point Algorithm for Inverse Strongly Monotone Operators and Maximal Monotone Operators in Banach Spaces1687-18201687-1812https://doaj.org/article/5dde2ad233ac4e6d86fc75410ea8cd112009-01-01T00:00:00Zhttp://www.fixedpointtheoryandapplications.com/content/2009/591874https://doaj.org/toc/1687-1820https://doaj.org/toc/1687-1812<p>Abstract</p> <p>We introduce an iterative scheme for finding a common element of the solution set of a maximal monotone operator and the solution set of the variational inequality problem for an inverse strongly-monotone operator in a uniformly smooth and uniformly convex Banach space, and then we prove weak and strong convergence theorems by using the notion of generalized projection. The result presented in this paper extend and improve the corresponding results of Kamimura et al. (2004), and Iiduka and Takahashi (2008). Finally, we apply our convergence theorem to the convex minimization problem, the problem of finding a zero point of a maximal monotone operator and the complementary problem.</p>Plubtieng SomyotSriprad WannaSpringerOpenarticleApplied mathematics. Quantitative methodsT57-57.97AnalysisQA299.6-433ENFixed Point Theory and Applications, Vol 2009, Iss 1, p 591874 (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 Plubtieng Somyot Sriprad Wanna An Extragradient Method and Proximal Point Algorithm for Inverse Strongly Monotone Operators and Maximal Monotone Operators in Banach Spaces
description	<p>Abstract</p> <p>We introduce an iterative scheme for finding a common element of the solution set of a maximal monotone operator and the solution set of the variational inequality problem for an inverse strongly-monotone operator in a uniformly smooth and uniformly convex Banach space, and then we prove weak and strong convergence theorems by using the notion of generalized projection. The result presented in this paper extend and improve the corresponding results of Kamimura et al. (2004), and Iiduka and Takahashi (2008). Finally, we apply our convergence theorem to the convex minimization problem, the problem of finding a zero point of a maximal monotone operator and the complementary problem.</p>
format	article
author	Plubtieng Somyot Sriprad Wanna
author_facet	Plubtieng Somyot Sriprad Wanna
author_sort	Plubtieng Somyot
title	An Extragradient Method and Proximal Point Algorithm for Inverse Strongly Monotone Operators and Maximal Monotone Operators in Banach Spaces
title_short	An Extragradient Method and Proximal Point Algorithm for Inverse Strongly Monotone Operators and Maximal Monotone Operators in Banach Spaces
title_full	An Extragradient Method and Proximal Point Algorithm for Inverse Strongly Monotone Operators and Maximal Monotone Operators in Banach Spaces
title_fullStr	An Extragradient Method and Proximal Point Algorithm for Inverse Strongly Monotone Operators and Maximal Monotone Operators in Banach Spaces
title_full_unstemmed	An Extragradient Method and Proximal Point Algorithm for Inverse Strongly Monotone Operators and Maximal Monotone Operators in Banach Spaces
title_sort	extragradient method and proximal point algorithm for inverse strongly monotone operators and maximal monotone operators in banach spaces
publisher	SpringerOpen
publishDate	2009
url	https://doaj.org/article/5dde2ad233ac4e6d86fc75410ea8cd11
work_keys_str_mv	AT plubtiengsomyot anextragradientmethodandproximalpointalgorithmforinversestronglymonotoneoperatorsandmaximalmonotoneoperatorsinbanachspaces AT sripradwanna anextragradientmethodandproximalpointalgorithmforinversestronglymonotoneoperatorsandmaximalmonotoneoperatorsinbanachspaces AT plubtiengsomyot extragradientmethodandproximalpointalgorithmforinversestronglymonotoneoperatorsandmaximalmonotoneoperatorsinbanachspaces AT sripradwanna extragradientmethodandproximalpointalgorithmforinversestronglymonotoneoperatorsandmaximalmonotoneoperatorsinbanachspaces
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An Extragradient Method and Proximal Point Algorithm for Inverse Strongly Monotone Operators and Maximal Monotone Operators in Banach Spaces

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