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A novel approach to the Jensen gap through Taylor's theorem
Author(s) -
Adil Khan Muhammad,
Khan Shahid,
Ullah Inam,
Ali Khan Khuram,
Chu YuMing
Publication year - 2020
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.6944
Subject(s) - mathematics , hadamard transform , hermite polynomials , upper and lower bounds , divergence (linguistics) , taylor series , taylor's theorem , identity (music) , mathematical analysis , pure mathematics , philosophy , linguistics , physics , acoustics
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.