Improvements of Jensen's inequality and its converse for strongly convex functions with applications to strongly f-divergences

In this paper, using the class of strongly convex functions, which is subclass of convex functions with stronger versions of analogous properties, we get improvements of Jessen's and Jensen's inequalities, their converses as well as related Jensen-type interpolating inequalities which pres...

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Bibliographic Details
Published in:	Journal of mathematical analysis and applications Vol. 531; no. 2; p. 127866
Main Author:	Ivelić Bradanović, Slavica
Format:	Journal Article
Language:	English
Published:	Elsevier Inc 15.03.2024
Subjects:	Csiszár f-divergence Jensen's inequality Jessen's inequality Kullback-Leibler divergence Strongly convex functions Strongly f-divergences Csiszár f-divergence Jensen's inequality Strongly convex functions Strongly f-divergences Kullback-Leibler divergence Jessen's inequality
ISSN:	0022-247X, 1096-0813
Online Access:	Get full text
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Summary:	In this paper, using the class of strongly convex functions, which is subclass of convex functions with stronger versions of analogous properties, we get improvements of Jessen's and Jensen's inequalities, their converses as well as related Jensen-type interpolating inequalities which present a starting point in many significant results in recent investigations. Obtained improvements we apply to so called strongly f-divergences, a concept of f-divergences for strongly convex functions. As outcome we derive stronger estimates for some well known divergences as the Kullback-Leibler divergence, χ2-divergence, Hellinger divergence, Bhattacharya distance and Jeffreys distance.
ISSN:	0022-247X 1096-0813
DOI:	10.1016/j.jmaa.2023.127866