Convergence of a proximal point algorithm for maximal monotone operators in Hilbert spaces

In this article, we consider the proximal point algorithm for the problem of approximating zeros of maximal monotone mappings. Strong convergence theorems for zero points of maximal monotone mappings are established in the framework of Hilbert spaces. 2000 AMS Subject Classification: 47H05; 47H09; 4...

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Published inJournal of inequalities and applications Vol. 2012; no. 1; p. 1
Main Authors Wei, Zhiqiang, Shi, Guohong
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 13.06.2012
Springer Nature B.V
Subjects
Analysis
Applications of Mathematics
Mathematics
Mathematics and Statistics
zero
nonexpansive mapping
maximal monotone mapping
fixed point
Online AccessGet full text
ISSN1029-242X
1025-5834
1029-242X
DOI10.1186/1029-242X-2012-137

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Abstract In this article, we consider the proximal point algorithm for the problem of approximating zeros of maximal monotone mappings. Strong convergence theorems for zero points of maximal monotone mappings are established in the framework of Hilbert spaces. 2000 AMS Subject Classification: 47H05; 47H09; 47J25.
AbstractList In this article, we consider the proximal point algorithm for the problem of approximating zeros of maximal monotone mappings. Strong convergence theorems for zero points of maximal monotone mappings are established in the framework of Hilbert spaces. 2000 AMS Subject Classification: 47H05; 47H09; 47J25.[PUBLICATION ABSTRACT]
In this article, we consider the proximal point algorithm for the problem of approximating zeros of maximal monotone mappings. Strong convergence theorems for zero points of maximal monotone mappings are established in the framework of Hilbert spaces. 2000 AMS Subject Classification: 47H05; 47H09; 47J25.
ArticleNumber 137
Author Wei, Zhiqiang
Shi, Guohong
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  fullname: Shi, Guohong
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  organization: College of Science, Hebei University of Engineering
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CitedBy_id crossref_primary_10_1186_1687_1812_2013_11
crossref_primary_10_1186_s40064_016_2389_9
Cites_doi 10.1016/j.cam.2009.07.018
10.1137/0329022
10.1016/j.cam.2010.01.015
10.1007/s10898-009-9410-6
10.1007/s10957-009-9615-3
10.1007/s11228-004-8196-4
10.1016/j.aml.2007.05.004
10.1016/S0362-546X(97)00606-8
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10.1016/j.na.2009.06.042
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ContentType Journal Article
Copyright Wei and Shi; licensee Springer. 2012. This article is published under license to BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License ( ), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Springer International Publishing AG 2012
Copyright_xml – notice: Wei and Shi; licensee Springer. 2012. This article is published under license to BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License ( ), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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Keywords zero
nonexpansive mapping
maximal monotone mapping
fixed point
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Snippet In this article, we consider the proximal point algorithm for the problem of approximating zeros of maximal monotone mappings. Strong convergence theorems for...
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SubjectTerms Analysis
Applications of Mathematics
Mathematics
Mathematics and Statistics
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Title Convergence of a proximal point algorithm for maximal monotone operators in Hilbert spaces
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