Probabilistic characterization of strong convexity
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.
Mathematics Subject Classification: 26A51, 26D15, 60E05, 60E15.