A novel approach to the Jensen gap through Taylor's theorem

Abstract

This article presents a new bound for the Jensen gap in classical as well as in generalized form through an integral identity deduced from Taylor's theorem. A discussion on the accuracy of the classical bound, through a numerical experiment, is a part of the paper. Also, the proposed bounds generate a bound for the Hermite–Hadamard gap and some reverses of the Hölder inequality. Finally, the paper deals with estimations of the Csiszár divergence and of some of its special cases.