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Enlarged Inclusion of Subdifferentials

Published online by Cambridge University Press:  20 November 2018

Lionel Thibault  and
Dariusz Zagrodny
Lionel Thibault
Affiliation:
Department of Mathematics, University Montpellier II, 34095 Montpellier, France
Dariusz Zagrodny
Affiliation:
Faculty of Mathemtics, and Natural Sciences, College of Sciences, Cardinal Stefan Wyszynski University, Warszawa 01-815, Poland
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Abstract

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This paper studies the integration of inclusion of subdifferentials. Under various verifiable conditions, we obtain that if two proper lower semicontinuous functions $f$ and $g$ have the subdifferential of $f$ included in the $\gamma $-enlargement of the subdifferential of $g$, then the difference of those functions is $\gamma $-Lipschitz over their effective domain.

Keywords

49J5246N1058C20subdifferentialdirectionally regular functionapproximate convex functionsubdifferentially and directionally stable function
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 48 , Issue 2 , 01 June 2005 , pp. 283 - 301
Copyright
Copyright © Canadian Mathematical Society 2005

References

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