Unifications of Continuous and Discrete Fractional Inequalities of the Hermite–Hadamard–Jensen–Mercer Type via Majorization
The main objective of the paper is to develop an innovative idea of bringing continuous and discrete inequalities into a unified form. The desired objective is thus obtained by embedding majorization theory with the existing notion of continuous inequalities. These notions are applied to the latest...
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| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2022-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2022/6964087 |
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| author | Shah Faisal Muhammad Adil Khan Tahir Ullah Khan Tareq Saeed Zaid Mohammmad Mohammad Mahdi Sayed |
| author_facet | Shah Faisal Muhammad Adil Khan Tahir Ullah Khan Tareq Saeed Zaid Mohammmad Mohammad Mahdi Sayed |
| author_sort | Shah Faisal |
| collection | DOAJ |
| description | The main objective of the paper is to develop an innovative idea of bringing continuous and discrete inequalities into a unified form. The desired objective is thus obtained by embedding majorization theory with the existing notion of continuous inequalities. These notions are applied to the latest generalized form of the inequalities, popularly known as the Hermite–Hadamard–Jensen–Mercer inequalities. Moreover, the frequently-used Caputo fractional operators are employed, which are rightly considered critical, especially for applied problems. Both weighted and unweighted forms of the developed results are discussed. In addition to this, some bounds are also provided for the absolute difference between the left- and right-sides of the main results. |
| format | Article |
| id | doaj-art-5e6e04139aaa44f9ac3c31917058095d |
| 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-5e6e04139aaa44f9ac3c31917058095d2025-02-03T06:01:17ZengWileyJournal of Function Spaces2314-88882022-01-01202210.1155/2022/6964087Unifications of Continuous and Discrete Fractional Inequalities of the Hermite–Hadamard–Jensen–Mercer Type via MajorizationShah Faisal0Muhammad Adil Khan1Tahir Ullah Khan2Tareq Saeed3Zaid Mohammmad Mohammad Mahdi Sayed4Department of MathematicsDepartment of MathematicsDepartment of MathematicsNonlinear Analysis and Applied Mathematics (NAAM)-Research GroupDepartment of MathematicsThe main objective of the paper is to develop an innovative idea of bringing continuous and discrete inequalities into a unified form. The desired objective is thus obtained by embedding majorization theory with the existing notion of continuous inequalities. These notions are applied to the latest generalized form of the inequalities, popularly known as the Hermite–Hadamard–Jensen–Mercer inequalities. Moreover, the frequently-used Caputo fractional operators are employed, which are rightly considered critical, especially for applied problems. Both weighted and unweighted forms of the developed results are discussed. In addition to this, some bounds are also provided for the absolute difference between the left- and right-sides of the main results.http://dx.doi.org/10.1155/2022/6964087 |
| spellingShingle | Shah Faisal Muhammad Adil Khan Tahir Ullah Khan Tareq Saeed Zaid Mohammmad Mohammad Mahdi Sayed Unifications of Continuous and Discrete Fractional Inequalities of the Hermite–Hadamard–Jensen–Mercer Type via Majorization Journal of Function Spaces |
| title | Unifications of Continuous and Discrete Fractional Inequalities of the Hermite–Hadamard–Jensen–Mercer Type via Majorization |
| title_full | Unifications of Continuous and Discrete Fractional Inequalities of the Hermite–Hadamard–Jensen–Mercer Type via Majorization |
| title_fullStr | Unifications of Continuous and Discrete Fractional Inequalities of the Hermite–Hadamard–Jensen–Mercer Type via Majorization |
| title_full_unstemmed | Unifications of Continuous and Discrete Fractional Inequalities of the Hermite–Hadamard–Jensen–Mercer Type via Majorization |
| title_short | Unifications of Continuous and Discrete Fractional Inequalities of the Hermite–Hadamard–Jensen–Mercer Type via Majorization |
| title_sort | unifications of continuous and discrete fractional inequalities of the hermite hadamard jensen mercer type via majorization |
| url | http://dx.doi.org/10.1155/2022/6964087 |
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