Historical Notes on Inequalities Ascribed to Hermite and Hadamard

The so-called Hermite-Hadamard inequalities are a fundamental result for convex functions defined on an interval of real numbers. They enjoy a natural geometric interpretation and offer a large number of applications for particular inequalities. In this paper we intend to investigate possible origins of the Hermite-Hadamard inequalities, showing their close connection with the midpoint and trapezoidal rules for numerical integration. The research offers a lot of historical notices, that might be of some interest apart from the considered inequalities. In particular, it appears clearly the inequalities were known long before the contributions by Hermite and Hadamard. Stampato nel mese di Dicembre 2004 presso il Centro Stamp