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’...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
AIMS Press
2020-06-01
|
| Series: | AIMS Mathematics |
| Subjects: | |
| Online Access: | https://www.aimspress.com/article/10.3934/math.2020315/fulltext.html |
| _version_ | 1818162697101901824 |
|---|---|
| author | Muhammad Adil Khan Josip Pečarić Yu-Ming Chu |
| author_facet | Muhammad Adil Khan Josip Pečarić Yu-Ming Chu |
| author_sort | Muhammad Adil Khan |
| collection | DOAJ |
| 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. |
| first_indexed | 2024-12-11T16:37:47Z |
| format | Article |
| id | doaj.art-3fe3a0686ccb445d889ece3fae7e1585 |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-12-11T16:37:47Z |
| publishDate | 2020-06-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-3fe3a0686ccb445d889ece3fae7e15852022-12-22T00:58:24ZengAIMS 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 |
| 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 |
| title | 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_short | Refinements of Jensen’s and McShane’s inequalities with applications |
| title_sort | refinements of jensen s and mcshane s inequalities with applications |
| 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 |