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Journal of Convex Analysis 20 (2013), No. 3, 655--668
Copyright Heldermann Verlag 2013

Strongly Adequate Functions on Banach Spaces

Michel Volle
Dép. de Mathématiques, Université d'Avignon et des Pays de Vaucluse, 74 Rue Louis Pasteur, 84029 Avignon, France

Constantin Zalinescu
University Alexandru Ioan Cuza, Faculty of Mathematics, Iasi, Romania
and: Institute of Mathematics O. Mayer, Iasi, Romania

The notion of adequate function has been recently introduced in order to characterize the essentially strictly convex functions on a reflexive Banach space among the weakly lower semicontinuous ones. In this paper we reinforce this concept and show that a lower semicontinuous function is essentially firmly subdifferentiable if and only if it is strongly adequate.

Keywords: Convex duality, well posed minimization problem, essential firm subdifferentiability, essential strong convexity, essential Frechet differentiability, total convexity, E-space.

MSC: 46G05, 49J50, 46N10

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