Bounds for the Jensen Gap in terms of Power Means with Applications

Jensen’s and its related inequalities have attracted the attention of several mathematicians due to the fact that Jensen’s inequality has numerous applications in almost all disciplines of mathematics and in other fields of science. In this article, we propose new bounds for the difference of two si...

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Autores principales:	Xuexiao You, Muhammad Adil Khan, Hamid Reza Moradi
Formato:	article
Lenguaje:	EN
Publicado:	Hindawi Limited 2021
Materias:	Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/7870763a1cb74deaa3348ee7b92d0f30
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spelling	oai:doaj.org-article:7870763a1cb74deaa3348ee7b92d0f302021-11-08T02:36:57ZBounds for the Jensen Gap in terms of Power Means with Applications2314-888810.1155/2021/1388843https://doaj.org/article/7870763a1cb74deaa3348ee7b92d0f302021-01-01T00:00:00Zhttp://dx.doi.org/10.1155/2021/1388843https://doaj.org/toc/2314-8888Jensen’s and its related inequalities have attracted the attention of several mathematicians due to the fact that Jensen’s inequality has numerous applications in almost all disciplines of mathematics and in other fields of science. In this article, we propose new bounds for the difference of two sides of Jensen’s inequality in terms of power means. An example has been presented for the importance and support of the main results. Related results have been given in quantum calculus. As consequences, improvements of quantum integral version of Hermite-Hadamard inequality have been derived. The obtained inequalities have been applied for some well-known inequalities such as Hermite-Hadamrd, Hölder, and power mean inequalities. Finally, some applications are given in information theory. The tools performed for obtaining the main results may be applied to obtain more results for other inequalities.Xuexiao YouMuhammad Adil KhanHamid Reza MoradiHindawi LimitedarticleMathematicsQA1-939ENJournal of Function Spaces, Vol 2021 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Mathematics QA1-939
spellingShingle	Mathematics QA1-939 Xuexiao You Muhammad Adil Khan Hamid Reza Moradi Bounds for the Jensen Gap in terms of Power Means with Applications
description	Jensen’s and its related inequalities have attracted the attention of several mathematicians due to the fact that Jensen’s inequality has numerous applications in almost all disciplines of mathematics and in other fields of science. In this article, we propose new bounds for the difference of two sides of Jensen’s inequality in terms of power means. An example has been presented for the importance and support of the main results. Related results have been given in quantum calculus. As consequences, improvements of quantum integral version of Hermite-Hadamard inequality have been derived. The obtained inequalities have been applied for some well-known inequalities such as Hermite-Hadamrd, Hölder, and power mean inequalities. Finally, some applications are given in information theory. The tools performed for obtaining the main results may be applied to obtain more results for other inequalities.
format	article
author	Xuexiao You Muhammad Adil Khan Hamid Reza Moradi
author_facet	Xuexiao You Muhammad Adil Khan Hamid Reza Moradi
author_sort	Xuexiao You
title	Bounds for the Jensen Gap in terms of Power Means with Applications
title_short	Bounds for the Jensen Gap in terms of Power Means with Applications
title_full	Bounds for the Jensen Gap in terms of Power Means with Applications
title_fullStr	Bounds for the Jensen Gap in terms of Power Means with Applications
title_full_unstemmed	Bounds for the Jensen Gap in terms of Power Means with Applications
title_sort	bounds for the jensen gap in terms of power means with applications
publisher	Hindawi Limited
publishDate	2021
url	https://doaj.org/article/7870763a1cb74deaa3348ee7b92d0f30
work_keys_str_mv	AT xuexiaoyou boundsforthejensengapintermsofpowermeanswithapplications AT muhammadadilkhan boundsforthejensengapintermsofpowermeanswithapplications AT hamidrezamoradi boundsforthejensengapintermsofpowermeanswithapplications
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Bounds for the Jensen Gap in terms of Power Means with Applications

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