Improvements of the integral Jensen inequality through the treatment of the concept of convexity of thrice differential functions
Jensen's inequality, with its broad applications across various fields, presents an important subject for investigation and research. In this article, we introduce novel enhancements to Jensen's inequality by utilizing the convexity properties of a thrice differentiable function in the abs...
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| Format: | Article |
| Language: | English |
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AIMS Press
2024-12-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.20241620 |
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| author | Asadullah Sohail Muhammad Adil Khan Xiaoye Ding Mohamed Sharaf Mohammed A. El-Meligy |
| author_facet | Asadullah Sohail Muhammad Adil Khan Xiaoye Ding Mohamed Sharaf Mohammed A. El-Meligy |
| author_sort | Asadullah Sohail |
| collection | DOAJ |
| description | Jensen's inequality, with its broad applications across various fields, presents an important subject for investigation and research. In this article, we introduce novel enhancements to Jensen's inequality by utilizing the convexity properties of a thrice differentiable function in the absolute sense. We conducted numerical experiments to compare our primary results with previously established findings. Additionally, we provided several applications of our major results to classical inequalities, means, and divergences. |
| format | Article |
| id | doaj-art-51ffd83500f54aacb2f5c6926961ea11 |
| institution | Kabale University |
| issn | 2473-6988 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj-art-51ffd83500f54aacb2f5c6926961ea112025-01-23T07:53:25ZengAIMS PressAIMS Mathematics2473-69882024-12-01912339733399410.3934/math.20241620Improvements of the integral Jensen inequality through the treatment of the concept of convexity of thrice differential functionsAsadullah Sohail0Muhammad Adil Khan1Xiaoye Ding2Mohamed Sharaf3Mohammed A. El-Meligy4Department of Mathematics, University of Peshawar, Peshawar 25000, PakistanDepartment of Mathematics, University of Peshawar, Peshawar 25000, PakistanGeneral Education Department, Anhui Xinhua University, Hefei 230088, ChinaIndustrial Engineering Department, College of Engineering, King Saud University, P.O. Box 800, Riyadh 11421, Saudi ArabiaApplied Science Research Center, Applied Science Private University, Amman, JordanJensen's inequality, with its broad applications across various fields, presents an important subject for investigation and research. In this article, we introduce novel enhancements to Jensen's inequality by utilizing the convexity properties of a thrice differentiable function in the absolute sense. We conducted numerical experiments to compare our primary results with previously established findings. Additionally, we provided several applications of our major results to classical inequalities, means, and divergences.https://www.aimspress.com/article/doi/10.3934/math.20241620convex functionconcave functionjensen's inequalityhölder inequality |
| spellingShingle | Asadullah Sohail Muhammad Adil Khan Xiaoye Ding Mohamed Sharaf Mohammed A. El-Meligy Improvements of the integral Jensen inequality through the treatment of the concept of convexity of thrice differential functions AIMS Mathematics convex function concave function jensen's inequality hölder inequality |
| title | Improvements of the integral Jensen inequality through the treatment of the concept of convexity of thrice differential functions |
| title_full | Improvements of the integral Jensen inequality through the treatment of the concept of convexity of thrice differential functions |
| title_fullStr | Improvements of the integral Jensen inequality through the treatment of the concept of convexity of thrice differential functions |
| title_full_unstemmed | Improvements of the integral Jensen inequality through the treatment of the concept of convexity of thrice differential functions |
| title_short | Improvements of the integral Jensen inequality through the treatment of the concept of convexity of thrice differential functions |
| title_sort | improvements of the integral jensen inequality through the treatment of the concept of convexity of thrice differential functions |
| topic | convex function concave function jensen's inequality hölder inequality |
| url | https://www.aimspress.com/article/doi/10.3934/math.20241620 |
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