Refined Young Inequality and Its Application to Divergences

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 studied some properties on the difference between the weighted arithmetic mean and the weighted geometric me...

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Detalles Bibliográficos
Autores principales: Furuichi, Shigeru, Minculete, Nicuşor
Formato: Online Artículo Texto
Lenguaje:English
Publicado: MDPI 2021
Materias:
Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8145510/
https://www.ncbi.nlm.nih.gov/pubmed/33922636
http://dx.doi.org/10.3390/e23050514
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author Furuichi, Shigeru
Minculete, Nicuşor
author_facet Furuichi, Shigeru
Minculete, Nicuşor
author_sort Furuichi, Shigeru
collection PubMed
description 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 studied 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.
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spelling pubmed-81455102021-05-26 Refined Young Inequality and Its Application to Divergences Furuichi, Shigeru Minculete, Nicuşor Entropy (Basel) Article 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 studied 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. MDPI 2021-04-23 /pmc/articles/PMC8145510/ /pubmed/33922636 http://dx.doi.org/10.3390/e23050514 Text en © 2021 by the authors. https://creativecommons.org/licenses/by/4.0/Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).
spellingShingle Article
Furuichi, Shigeru
Minculete, Nicuşor
Refined Young Inequality and Its Application to Divergences
title Refined Young Inequality and Its Application to Divergences
title_full Refined Young Inequality and Its Application to Divergences
title_fullStr Refined Young Inequality and Its Application to Divergences
title_full_unstemmed Refined Young Inequality and Its Application to Divergences
title_short Refined Young Inequality and Its Application to Divergences
title_sort refined young inequality and its application to divergences
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8145510/
https://www.ncbi.nlm.nih.gov/pubmed/33922636
http://dx.doi.org/10.3390/e23050514
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