Refined Young inequality and its application to divergences
arXiv:2104.12925 · doi:10.3390/e23050514
Abstract
We give bounds on the difference between the weighted arithmetic mean and the weighted geometric mean. These imply refined Young inequalities and the reverses of the Young inequality. We also study some properties on the difference between the weighted arithmetic mean and the weighted geometric mean. Applying the newly obtained inequalities, we show some results on the Tsallis divergence, the Rényi divergence, the Jeffreys-Tsallis divergence and the Jensen-Shannon-Tsallis divergence.
16 pages
References in corpus (8)
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- Fundamental properties of Tsallis relative entropy
- Information theoretical properties of Tsallis entropies
- Mathematical inequalities for some divergences
- Alternative reverse inequalities for Young's inequality
- An equivalent form of Young's inequality with upper bound
- Inequalities related to some types of entropies and divergences
- Generalized reverse Young and Heinz inequalities