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arXiv · 2611.02518

Jensen--Mercer-type Inequalities and Strongly $f$-Divergences

Vidyanshu Kumar Rai·Ravinder Kumar
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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, $χ^{2}$-divergence, Hellinger divergence, Bhattacharyya-type divergence, and Jeffreys divergence.

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Vidyanshu Kumar Rai, Ravinder Kumar. 2026-11-02. Jensen--Mercer-type Inequalities and Strongly $f$-Divergences. https://arxiv.org/abs/2611.02518

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