Geodesic
Strongly Adequate Functions on Banach Spaces
Journal of convex analysis, Tome 20 (2013) no. 3, pp. 655-668
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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.
Classification : 46G05, 49J50, 46N10
Mots-clés : Convex duality, well posed minimization problem, essential firm subdifferentiability, essential strong convexity, essential Frechet differentiability, total convexity, E-space 
@article{JCA_2013_20_3_JCA_2013_20_3_a2,
     author = {M. Volle and C. Zalinescu},
     title = {Strongly {Adequate} {Functions} on {Banach} {Spaces}},
     journal = {Journal of convex analysis},
     pages = {655--668},
     year = {2013},
     volume = {20},
     number = {3},
     url = {http://geodesic.mathdoc.fr/item/JCA_2013_20_3_JCA_2013_20_3_a2/}
}
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M. Volle; C. Zalinescu. Strongly Adequate Functions on Banach Spaces. Journal of convex analysis, Tome 20 (2013) no. 3, pp. 655-668. http://geodesic.mathdoc.fr/item/JCA_2013_20_3_JCA_2013_20_3_a2/