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...
Saved in:
| Main Authors: | , , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2021-01-01
|
| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2021/1951799 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832561361590157312 |
|---|---|
| author | Yongping Deng Hidayat Ullah Muhammad Adil Khan Sajid Iqbal Shanhe Wu |
| author_facet | Yongping Deng Hidayat Ullah Muhammad Adil Khan Sajid Iqbal Shanhe Wu |
| author_sort | Yongping Deng |
| collection | DOAJ |
| 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. |
| format | Article |
| id | doaj-art-6bd2af6fc3e34d26aa135e83076d4389 |
| institution | Kabale University |
| issn | 2314-4629 2314-4785 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-6bd2af6fc3e34d26aa135e83076d43892025-02-03T01:25:09ZengWileyJournal of Mathematics2314-46292314-47852021-01-01202110.1155/2021/19517991951799Refinements of Jensen’s Inequality via Majorization Results with Applications in the Information TheoryYongping Deng0Hidayat Ullah1Muhammad Adil Khan2Sajid Iqbal3Shanhe Wu4Department of Mathematics, Longyan University, Longyan 364012, ChinaDepartment of Mathematics, University of Peshawar, Peshawar 25000, PakistanDepartment of Mathematics, University of Peshawar, Peshawar 25000, PakistanDepartment of Mathematics, Riphah International University, Faisalabad Campus, Satyana Road, Faisalabad, PakistanDepartment of Mathematics, Longyan University, Longyan 364012, ChinaIn 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 |
| 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 |
| title | 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_short | 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 |
| url | http://dx.doi.org/10.1155/2021/1951799 |
| work_keys_str_mv | AT yongpingdeng refinementsofjensensinequalityviamajorizationresultswithapplicationsintheinformationtheory AT hidayatullah refinementsofjensensinequalityviamajorizationresultswithapplicationsintheinformationtheory AT muhammadadilkhan refinementsofjensensinequalityviamajorizationresultswithapplicationsintheinformationtheory AT sajidiqbal refinementsofjensensinequalityviamajorizationresultswithapplicationsintheinformationtheory AT shanhewu refinementsofjensensinequalityviamajorizationresultswithapplicationsintheinformationtheory |