Refinements of Jensen’s and McShane’s inequalities with applications

In this article, we consider the generalized forms of the Jensen’s inequality given by Jessen and McShane for isotonic linear functionals, derive several refinements for the Jessen’s and McShane’s inequalities connected to certain functions from the linear space, generalize the Jessen’s and McShane’...

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Main Authors:	Muhammad Adil Khan, Josip Pečarić, Yu-Ming Chu
Format:	Article
Language:	English
Published:	AIMS Press 2020-06-01
Series:	AIMS Mathematics
Subjects:	jensen’s inequality convex function linear functional mcshane’s inequality hölder inequality beck’s inequality
Online Access:	https://www.aimspress.com/article/10.3934/math.2020315/fulltext.html

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spelling	doaj-3fe3a0686ccb445d889ece3fae7e15852020-11-25T03:55:07ZengAIMS PressAIMS Mathematics2473-69882020-06-01554931494510.3934/math.2020315Refinements of Jensen’s and McShane’s inequalities with applicationsMuhammad Adil Khan0Josip Pečarić1Yu-Ming Chu21 Department of Mathematics, University of Peshawar, Peshawar 25000, Pakistan2 Russian Peoples’ Friendship University, 117198 Moscow, Russia3 Department of Mathematics, Huzhou University, Huzhou 313000, P. R. China 4 Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering, Changsha University of Science & Technology, Changsha 410114, P. R. ChinaIn this article, we consider the generalized forms of the Jensen’s inequality given by Jessen and McShane for isotonic linear functionals, derive several refinements for the Jessen’s and McShane’s inequalities connected to certain functions from the linear space, generalize the Jessen’s and McShane’s inequalities pertaining n certain functions. As applications, we provide some improvements for the generalized means, Holder and generalized Beck’s inequalities.https://www.aimspress.com/article/10.3934/math.2020315/fulltext.htmljensen’s inequalityconvex functionlinear functionalmcshane’s inequalityhölder inequalitybeck’s inequality
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Muhammad Adil Khan Josip Pečarić Yu-Ming Chu
spellingShingle	Muhammad Adil Khan Josip Pečarić Yu-Ming Chu Refinements of Jensen’s and McShane’s inequalities with applications AIMS Mathematics jensen’s inequality convex function linear functional mcshane’s inequality hölder inequality beck’s inequality
author_facet	Muhammad Adil Khan Josip Pečarić Yu-Ming Chu
author_sort	Muhammad Adil Khan
title	Refinements of Jensen’s and McShane’s inequalities with applications
title_short	Refinements of Jensen’s and McShane’s inequalities with applications
title_full	Refinements of Jensen’s and McShane’s inequalities with applications
title_fullStr	Refinements of Jensen’s and McShane’s inequalities with applications
title_full_unstemmed	Refinements of Jensen’s and McShane’s inequalities with applications
title_sort	refinements of jensen’s and mcshane’s inequalities with applications
publisher	AIMS Press
series	AIMS Mathematics
issn	2473-6988
publishDate	2020-06-01
description	In this article, we consider the generalized forms of the Jensen’s inequality given by Jessen and McShane for isotonic linear functionals, derive several refinements for the Jessen’s and McShane’s inequalities connected to certain functions from the linear space, generalize the Jessen’s and McShane’s inequalities pertaining n certain functions. As applications, we provide some improvements for the generalized means, Holder and generalized Beck’s inequalities.
topic	jensen’s inequality convex function linear functional mcshane’s inequality hölder inequality beck’s inequality
url	https://www.aimspress.com/article/10.3934/math.2020315/fulltext.html
work_keys_str_mv	AT muhammadadilkhan refinementsofjensensandmcshanesinequalitieswithapplications AT josippecaric refinementsofjensensandmcshanesinequalitieswithapplications AT yumingchu refinementsofjensensandmcshanesinequalitieswithapplications
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Refinements of Jensen’s and McShane’s inequalities with applications

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