Refinements of Jensen’s Inequality via Majorization Results with Applications in the Information Theory

Refinements of Jensen’s Inequality via Majorization Results with Applications in the Information Theory

In this study, we present some new refinements of the Jensen inequality with the help of majorization results. We use the concept of convexity along with the theory of majorization and obtain refinements of the Jensen inequality. Moreover, as consequences of the refined Jensen inequality, we derive...

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Main Authors: Yongping Deng, Hidayat Ullah, Muhammad Adil Khan, Sajid Iqbal, Shanhe Wu
Format: Article
Language:English
Published: Hindawi Limited 2021-01-01
Series:Journal of Mathematics
Online Access:http://dx.doi.org/10.1155/2021/1951799
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spelling doaj-6bd2af6fc3e34d26aa135e83076d43892021-08-30T00:00:37ZengHindawi LimitedJournal of Mathematics2314-47852021-01-01202110.1155/2021/1951799Refinements of Jensen’s Inequality via Majorization Results with Applications in the Information TheoryYongping Deng0Hidayat Ullah1Muhammad Adil Khan2Sajid Iqbal3Shanhe Wu4Department of MathematicsDepartment of MathematicsDepartment of MathematicsDepartment of MathematicsDepartment of MathematicsIn this study, we present some new refinements of the Jensen inequality with the help of majorization results. We use the concept of convexity along with the theory of majorization and obtain refinements of the Jensen inequality. Moreover, as consequences of the refined Jensen inequality, we derive some bounds for power means and quasiarithmetic means. Furthermore, as applications of the refined Jensen inequality, we give some bounds for divergences, Shannon entropy, and various distances associated with probability distributions.http://dx.doi.org/10.1155/2021/1951799
collection DOAJ
language English
format Article
sources DOAJ
author Yongping Deng
Hidayat Ullah
Muhammad Adil Khan
Sajid Iqbal
Shanhe Wu
spellingShingle Yongping Deng
Hidayat Ullah
Muhammad Adil Khan
Sajid Iqbal
Shanhe Wu
Refinements of Jensen’s Inequality via Majorization Results with Applications in the Information Theory
Journal of Mathematics
author_facet Yongping Deng
Hidayat Ullah
Muhammad Adil Khan
Sajid Iqbal
Shanhe Wu
author_sort Yongping Deng
title Refinements of Jensen’s Inequality via Majorization Results with Applications in the Information Theory
title_short Refinements of Jensen’s Inequality via Majorization Results with Applications in the Information Theory
title_full Refinements of Jensen’s Inequality via Majorization Results with Applications in the Information Theory
title_fullStr Refinements of Jensen’s Inequality via Majorization Results with Applications in the Information Theory
title_full_unstemmed Refinements of Jensen’s Inequality via Majorization Results with Applications in the Information Theory
title_sort refinements of jensen’s inequality via majorization results with applications in the information theory
publisher Hindawi Limited
series Journal of Mathematics
issn 2314-4785
publishDate 2021-01-01
description In this study, we present some new refinements of the Jensen inequality with the help of majorization results. We use the concept of convexity along with the theory of majorization and obtain refinements of the Jensen inequality. Moreover, as consequences of the refined Jensen inequality, we derive some bounds for power means and quasiarithmetic means. Furthermore, as applications of the refined Jensen inequality, we give some bounds for divergences, Shannon entropy, and various distances associated with probability distributions.
url http://dx.doi.org/10.1155/2021/1951799
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AT hidayatullah refinementsofjensensinequalityviamajorizationresultswithapplicationsintheinformationtheory
AT muhammadadilkhan refinementsofjensensinequalityviamajorizationresultswithapplicationsintheinformationtheory
AT sajidiqbal refinementsofjensensinequalityviamajorizationresultswithapplicationsintheinformationtheory
AT shanhewu refinementsofjensensinequalityviamajorizationresultswithapplicationsintheinformationtheory
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