On the Fitzpatrick transform of a monotone bifunction

A new definition of monotone bifunctions is given, which is a slight generalization of the original definition given by Blum and Oettli, but which is better suited for relating monotone bifunctions to monotone operators. In this new definition, the Fitzpatrick transform of a maximal monotone bifunct...

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Bibliographic Details
Published inOptimization Vol. 62; no. 6; pp. 693 - 701
Main Authors Alizadeh, M.H., Hadjisavvas, N.
Format Journal Article
LanguageEnglish
Published Philadelphia Taylor & Francis Group 01.06.2013
Taylor & Francis LLC
Subjects
Construction
Convex analysis
equilibrium problem
Fitzpatrick function
Mathematical analysis
maximal monotone operator
monotone bifunction
Operators
Optimization
Studies
Transforms
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Summary:A new definition of monotone bifunctions is given, which is a slight generalization of the original definition given by Blum and Oettli, but which is better suited for relating monotone bifunctions to monotone operators. In this new definition, the Fitzpatrick transform of a maximal monotone bifunction is introduced so as to correspond exactly to the Fitzpatrick function of a maximal monotone operator in case the bifunction is constructed starting from the operator. Whenever the monotone bifunction is lower semicontinuous and convex with respect to its second variable, the Fitzpatrick transform permits to obtain results on its maximal monotonicity.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
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content type line 23
ISSN:0233-1934
1029-4945
DOI:10.1080/02331934.2011.653975