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Journal of Convex Analysis 09 (2002), No. 2, 601--607
Copyright Heldermann Verlag 2002

Lipschitzian Behavior of the Fenchel Biconjugacy

Jean-Paul Penot
Dép. des Mathématiques, Université de Pau, 64000 Pau, France

We present sufficient conditions ensuring that the Legendre-Young-Fenchel biconjugacy is locally Lipschizian. An application to the continuity of some operations on the space of subsets of an Euclidean space is given.

Keywords: Bipolar, conjugacy, biconjugate, convex set, excess, Fenchel transform, Hausdorff distance, Minkowski difference, support function.

MSC: 26E25, 49J53; 52A20, 54C60, 52A05

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