Geodesic
The infima of functionals of a special kind on a compact convex set
Sibirskij žurnal industrialʹnoj matematiki, Tome 8 (2005) no. 4, pp. 91-99 
V. Ya. Prudnikov. The infima of functionals of a special kind on a compact convex set. Sibirskij žurnal industrialʹnoj matematiki, Tome 8 (2005) no. 4, pp. 91-99. http://geodesic.mathdoc.fr/item/SJIM_2005_8_4_a7/
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     title = {The infima of functionals of a~special kind on a~compact convex set},
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Voir la notice de l'article provenant de la source Math-Net.Ru

It is proved that the infimum of the ratio of a concave functional and a convex functional is attained at the extreme points of a compact convex set in a normed linear space. A criterion for the membership of a given element in the set of extreme points is proposed and the existence of a strongly convex functional on a compact set is shown.

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