Minimal antiderivatives and monotonicity
type: Item
instance of: scholarly article
title: Minimal antiderivatives and monotonicity
zbMATH Open document ID: 1251.47046
author: Sedi Bartz
author: Simeon Reich
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2010-11-05T00:00:00Z
review text: The authors study convex analytic frameworks which give rise to families of convex functions that contain their lower envelope. For a certain partial data regarding a subdifferential being given, they consider the family of all convex antiderivatives that comply with the given data. They prove that this family is non-empty and, specifically, contains a minimal antiderivative, in a rather general setting. Duality properties of representing functions are also captured, and the gap between the Fitzpatrick function and the Fitzpatrick family is filled by this notion of minimality of the Fitzpatrick function.
reviewed by: K. C. Sivakumar
Mathematics Subject Classification ID: 47H05
Mathematics Subject Classification ID: 52A41
Mathematics Subject Classification ID: 90C25
zbMATH DE Number: 5810940
zbMATH Keywords: convex function
zbMATH Keywords: cyclically monotone operator
zbMATH Keywords: Fitzpatrick function
zbMATH Keywords: maximal monotone operator
zbMATH Keywords: minimal antiderivative
zbMATH Keywords: subdifferential operator
MaRDI profile type: Publication
full work available at URL: j.na.2010.08.015
OpenAlex ID: W1975422714
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DOI: 10.1016/J.NA.2010.08.015
description: scientific article; zbMATH DE number 5810940