This article is cited in 4 papers

The infima of functionals of a special kind on a compact convex set

V. Ya. Prudnikov

Khabarovsk State University of Technology

Abstract: 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.

UDC: 519.85

Received: 24.01.2005
Revised: 05.05.2005

 English version: Journal of Applied and Industrial Mathematics, 2007, 1:2, 217–224

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