Probabilistic characterization of strong convexity

Abstract

Tyt. z nagł.References p. 103.Dostępny również w formie drukowanej.ABSTRACT: Strong convexity is considered for real functions defined on a real interval. Probabilistic characterization is given and its geometrical sense is explained. Using this characterization some inequalities of Jensen-type are obtained. KEYWORDS: convexity, strong convexity, Jensen's inequality, Jensen gap of a function, distribution of a random variable, variance