Abstract

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.

Author information

Contact details are reproduced from the original publication and may be historical.

Michel Volle

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

Michel.Volle@univ-avignon.fr

Constantin Zalinescu

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

zalinesc@uaic.ro

Keywords

  • Convex duality
  • well posed minimization problem
  • essential firm subdifferentiability
  • essential strong convexity
  • essential Frechet differentiability
  • total convexity
  • E-space

Mathematics Subject Classification

46G05, 49J50, 46N10

Suggested citation

M. Volle, C. Zalinescu. “Strongly Adequate Functions on Banach Spaces.” Journal of Convex Analysis 20 (2013), No. 3, 655–668.

Copyright Heldermann Verlag 2013