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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Main Authors: Xuexiao You, Muhammad Adil Khan, Hamid Reza Moradi
Format: Article
Language:English
Published: Wiley 2021-01-01
Series:Journal of Function Spaces
Online Access:http://dx.doi.org/10.1155/2021/1388843
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author Xuexiao You
Muhammad Adil Khan
Hamid Reza Moradi
author_facet Xuexiao You
Muhammad Adil Khan
Hamid Reza Moradi
author_sort Xuexiao You
collection DOAJ
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.
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institution Kabale University
issn 2314-8888
language English
publishDate 2021-01-01
publisher Wiley
record_format Article
series Journal of Function Spaces
spelling doaj-art-7870763a1cb74deaa3348ee7b92d0f302025-02-03T06:43:54ZengWileyJournal of Function Spaces2314-88882021-01-01202110.1155/2021/1388843Bounds for the Jensen Gap in terms of Power Means with ApplicationsXuexiao You0Muhammad Adil Khan1Hamid Reza Moradi2School of Mathematics and StatisticsDepartment of MathematicsDepartment of MathematicsJensen’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.http://dx.doi.org/10.1155/2021/1388843
spellingShingle Xuexiao You
Muhammad Adil Khan
Hamid Reza Moradi
Bounds for the Jensen Gap in terms of Power Means with Applications
Journal of Function Spaces
title 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_short 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
url http://dx.doi.org/10.1155/2021/1388843
work_keys_str_mv AT xuexiaoyou boundsforthejensengapintermsofpowermeanswithapplications
AT muhammadadilkhan boundsforthejensengapintermsofpowermeanswithapplications
AT hamidrezamoradi boundsforthejensengapintermsofpowermeanswithapplications