A novel approach to the Jensen gap through Taylor's theorem. (14th October 2020)

• Record Type: Journal Article
• Authors: Adil Khan, Muhammad; Khan, Shahid; Ullah, Inam; Ali Khan, Khuram; Chu, Yu‐Ming
• Is Part Of: Mathematical methods in the applied sciences. Volume 44:Number 5(2021)
• Page Start: 3324
• Page End: 3333
• Publication Date: 2020-10-14
• Subjects: convex function -- csiszár divergence -- Hermite–Hadamard inequality -- Hölder inequality -- Jensen inequality -- Taylor's theorem; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.6944
• Languages: English
• ISSNs: 0170-4214

Abstract

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.