Refined Young inequality and its application to divergences
Classical Analysis and ODEs
2021-04-28 v1 Statistical Mechanics
Information Theory
math.IT
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 R\'{e}nyi divergence, the Jeffreys-Tsallis divergence and the Jensen-Shannon-Tsallis divergence.
Keywords
Cite
@article{arxiv.2104.12925,
title = {Refined Young inequality and its application to divergences},
author = {Shigeru Furuichi and Nicuşor Minculete},
journal= {arXiv preprint arXiv:2104.12925},
year = {2021}
}
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16 pages