Journal of Convex Analysis 08 (2001), No. 1, 127--148
Copyright Heldermann Verlag 2001
A Characterization of Convex and Semicoercive Functionals
Samir Adly
LACO, Université de Limoges, 123 Avenue A. Thomas, 87060 Limoges, France
Emil Ernst
Institute of Mathematics, Romanian Academy of Sciences, 70700 Bucharest, Romania
Michel Théra
Université de Limoges, 123 Avenue A. Thomas, 87060 Limoges, France
We prove that every proper convex and lower semicontinuous functional Φ defined on a real reflexive Banach space X is semicoercive if and only if every small uniform perturbation of Φ attains its minimum value on X.
Keywords: Convex analysis, barrier cone, support functional, recession analysis, semicoercive functional.
MSC: 49J40
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