A CRITERION FOR THE CONVERSE OF THE HERMITE-HADAMARD INEQUALITY ON SIMPLICES

摘要

It is already known that if a function satisfies the left or the right Hennite-Hadaniard inequality for all simplices in its domain of definition, then it is convex, provided that the density of the measure is continuous and does not vanish identically on any segment. Here we show that this condition can be relaxed.