Some Applications of a Theorem on Convex Functions

摘要

This paper presents several applications of the theory developed elsewhere (AD-603 820). The results established here depend upon a fundamental theorem on convex functions, previously used in relation to the Theory of Games. Certain extensions of Helly's theorem, approximation and fitting results, and covering theorems for the n dimensional unit sphere are obtained. All these are intrinsically connected with one another. The authors believe they possess independent interest. (Author)