Some Improvements of Jensen’s Inequality via 4-Convexity and Applications
The intention of this note is to investigate some new important estimates for the Jensen gap while utilizing a 4-convex function. We use the Jensen inequality and definition of convex function in order to achieve the required estimates for the Jensen gap. We acquire new improvements of the Hölder an...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2022-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2022/2157375 |
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| _version_ | 1832549456546889728 |
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| author | Hidayat Ullah Muhammad Adil Khan Tareq Saeed Zaid Mohammed Mohammed Mahdi Sayed |
| author_facet | Hidayat Ullah Muhammad Adil Khan Tareq Saeed Zaid Mohammed Mohammed Mahdi Sayed |
| author_sort | Hidayat Ullah |
| collection | DOAJ |
| description | The intention of this note is to investigate some new important estimates for the Jensen gap while utilizing a 4-convex function. We use the Jensen inequality and definition of convex function in order to achieve the required estimates for the Jensen gap. We acquire new improvements of the Hölder and Hermite–Hadamard inequalities with the help of the main results. We discuss some interesting relations for quasi-arithmetic and power means as consequences of main results. At last, we give the applications of our main inequalities in the information theory. The approach and techniques used in the present note may simulate more research in this field. |
| format | Article |
| id | doaj-art-9e55915279164c609f73c982c9c41d32 |
| institution | Kabale University |
| issn | 2314-8888 |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-9e55915279164c609f73c982c9c41d322025-02-03T06:11:19ZengWileyJournal of Function Spaces2314-88882022-01-01202210.1155/2022/2157375Some Improvements of Jensen’s Inequality via 4-Convexity and ApplicationsHidayat Ullah0Muhammad Adil Khan1Tareq Saeed2Zaid Mohammed Mohammed Mahdi Sayed3Department of MathematicsDepartment of MathematicsNonlinear Analysis and Applied Mathematics- (NAAM-) Research GroupDepartment of MathematicsThe intention of this note is to investigate some new important estimates for the Jensen gap while utilizing a 4-convex function. We use the Jensen inequality and definition of convex function in order to achieve the required estimates for the Jensen gap. We acquire new improvements of the Hölder and Hermite–Hadamard inequalities with the help of the main results. We discuss some interesting relations for quasi-arithmetic and power means as consequences of main results. At last, we give the applications of our main inequalities in the information theory. The approach and techniques used in the present note may simulate more research in this field.http://dx.doi.org/10.1155/2022/2157375 |
| spellingShingle | Hidayat Ullah Muhammad Adil Khan Tareq Saeed Zaid Mohammed Mohammed Mahdi Sayed Some Improvements of Jensen’s Inequality via 4-Convexity and Applications Journal of Function Spaces |
| title | Some Improvements of Jensen’s Inequality via 4-Convexity and Applications |
| title_full | Some Improvements of Jensen’s Inequality via 4-Convexity and Applications |
| title_fullStr | Some Improvements of Jensen’s Inequality via 4-Convexity and Applications |
| title_full_unstemmed | Some Improvements of Jensen’s Inequality via 4-Convexity and Applications |
| title_short | Some Improvements of Jensen’s Inequality via 4-Convexity and Applications |
| title_sort | some improvements of jensen s inequality via 4 convexity and applications |
| url | http://dx.doi.org/10.1155/2022/2157375 |
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