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

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 gen...

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Bibliographic Details
Published in:Mathematical methods in the applied sciences 2021-03, Vol.44 (5), p.3324-3333
Main Authors: Adil Khan, Muhammad, Khan, Shahid, Ullah, Inam, Ali Khan, Khuram, Chu, Yu‐Ming
Format: Article
Language:English
Subjects:
convex function
csiszár divergence
Hermite–Hadamard inequality
Hölder inequality
Jensen inequality
Taylor's theorem
Theorems
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Summary: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.
ISSN:0170-4214
1099-1476
DOI:10.1002/mma.6944