A novel approach to the Jensen gap through Taylor's theorem. (14th October 2020) - Adil Khan, Muhammad; Khan, Shahid; Ullah, Inam; Ali Khan, Khuram; Chu, Yu‐Ming
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.