Old and new on the Hermite-Hadamard inequality
This paper is a survey of the results grown up from the Hermite-Hadamard inequality. Both, old and new results are presented, complemented and discussed within this framework. The Hermite-Hadamard inequality is presented in connection with subdifferentials and quadrature formulae; some improvements of it are discussed. Then a short account on classical Choquet theory is given; a generalization of it is presented, in the same spirit in which the Jensen-Steffensen inequality generalizes the Jensen inequality. A number of problems involving \(n\)-convex functions are discussed. This provides a framework to bring together many nice results, to compare, relate and extend them.
scientific article; zbMATH DE number 2151935