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A viability approach to the inverse set-valued map theorem

A viability approach to the inverse set-valued map theorem The purpose of this paper is to characterize by means of viability tools the pseudo-lipschitzianity property of a set-valued map F in a neighborhood of a point of its graph in terms of derivatives of this set-valued map F in a neighborhood of a point of its graph, instead of using the transposes of the derivatives. On the way, we relate these properties to the calmness index of a set-valued map, an extensions of Clarke’s calmness of a function, as well as Doyen’s Lipschitz kernel of a set-valued map, which is the largest Lipschitz submap. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Evolution Equations Springer Journals

A viability approach to the inverse set-valued map theorem

Journal of Evolution Equations , Volume 6 (3) – Aug 1, 2006

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References (19)

Publisher
Springer Journals
Copyright
Copyright © 2006 by Birkhäuser Verlag, Basel
Subject
Mathematics; Analysis
ISSN
1424-3199
eISSN
1424-3202
DOI
10.1007/s00028-006-0258-7
Publisher site
See Article on Publisher Site

Abstract

The purpose of this paper is to characterize by means of viability tools the pseudo-lipschitzianity property of a set-valued map F in a neighborhood of a point of its graph in terms of derivatives of this set-valued map F in a neighborhood of a point of its graph, instead of using the transposes of the derivatives. On the way, we relate these properties to the calmness index of a set-valued map, an extensions of Clarke’s calmness of a function, as well as Doyen’s Lipschitz kernel of a set-valued map, which is the largest Lipschitz submap.

Journal

Journal of Evolution EquationsSpringer Journals

Published: Aug 1, 2006

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