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.

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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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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/

[1] Gavurin M. K., Malozemov V. N., Ekstremalnye zadachi s lineinymi ogranicheniyami, Izd-vo LGU, L., 1984 | Zbl

[2] Pshenichnyi B. N., Neobkhodimye usloviya ekstremuma, Nauka, M., 1982 | MR

[3] Vasilev F. P., Metody resheniya ekstremalnykh zadach, Nauka, M., 1981 | MR

[4] Tikhomirov V. M., Nekotorye voprosy teorii priblizhenii, Izd-vo MGU, M., 1976 | MR

[5] Sadovnichii V. A., Teoriya operatorov, Vysshaya shkola, M., 1999

[6] Rudin U., Funktsionalnyi analiz, Mir, M., 1975 | MR