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Jensen--Mercer-type Inequalities and Strongly f-Divergences
Abstract
In this paper, we develop refined Jensen--Mercer-type inequalities for strongly convex functions, including reverse inequalities in the differentiable case. We identify the relationships between these inequalities and known bounds. Our method exploits a structural decomposition of strongly convex functions together with classical convexity arguments. As applications, we obtain explicit and computable bounds for strongly f-divergences, leading to new quantitative estimates for major divergence measures such as the Kullback--Leibler divergence, χ2-divergence, Hellinger divergence, Bhattacharyya-type divergence, and Jeffreys divergence.
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BibTeX
@misc{rai2026jensenmercertype,
title = {{Jensen--Mercer-type Inequalities and Strongly $f$-Divergences}},
author = {Vidyanshu Kumar Rai and Ravinder Kumar},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.02518},
eprint = {2611.02518},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.02518},
}
RIS
TY - UNPB
TI - Jensen--Mercer-type Inequalities and Strongly f-Divergences
AU - Vidyanshu Kumar Rai
AU - Ravinder Kumar
PY - 2026
DA - 2026/11/02
PB - arXiv
DO - 10.48550/arxiv.2611.02518
UR - https://arxiv.org/abs/2611.02518
AB - In this paper, we develop refined Jensen--Mercer-type inequalities for strongly convex functions, including reverse inequalities in the differentiable case. We identify the relationships between these inequalities and known bounds. Our method exploits a structural decomposition of strongly convex functions together with classical convexity arguments. As applications, we obtain explicit and computable bounds for strongly f-divergences, leading to new quantitative estimates for major divergence measures such as the Kullback--Leibler divergence, χ^2-divergence, Hellinger divergence, Bhattacharyya-type divergence, and Jeffreys divergence.
ER -