Some New Generalized Fractional Newton’s Type Inequalities for Convex Functions
In this paper, we establish some new Newton’s type inequalities for differentiable convex functions using the generalized Riemann-Liouville fractional integrals. The main edge of the newly established inequalities is that these can be turned into several new and existing inequalities for different f...
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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/10.1155/2022/6261970 |
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| _version_ | 1832553007124840448 |
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| author | Jarunee Soontharanon Muhammad Aamir Ali Hüseyin Budak Pinar Kösem Kamsing Nonlaopon Thanin Sitthiwirattham |
| author_facet | Jarunee Soontharanon Muhammad Aamir Ali Hüseyin Budak Pinar Kösem Kamsing Nonlaopon Thanin Sitthiwirattham |
| author_sort | Jarunee Soontharanon |
| collection | DOAJ |
| description | In this paper, we establish some new Newton’s type inequalities for differentiable convex functions using the generalized Riemann-Liouville fractional integrals. The main edge of the newly established inequalities is that these can be turned into several new and existing inequalities for different fractional integrals like Riemann-Liouville fractional integrals, k-fractional integrals, Katugampola fractional operators, conformable fractional operators, Hadamard fractional operators, and fractional operators with the exponential kernel without proving one by one. It is also shown that the newly established inequalities are the refinements of the previously established inequalities inside the literature. |
| format | Article |
| id | doaj-art-ba7df219230b40d5902971e9f1965fa6 |
| 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-ba7df219230b40d5902971e9f1965fa62025-02-03T05:57:23ZengWileyJournal of Function Spaces2314-88882022-01-01202210.1155/2022/6261970Some New Generalized Fractional Newton’s Type Inequalities for Convex FunctionsJarunee Soontharanon0Muhammad Aamir Ali1Hüseyin Budak2Pinar Kösem3Kamsing Nonlaopon4Thanin Sitthiwirattham5Department of MathematicsJiangsu Key Laboratory for NSLSCSDepartment of MathematicsDepartment of MathematicsDepartment of MathematicsMathematics DepartmentIn this paper, we establish some new Newton’s type inequalities for differentiable convex functions using the generalized Riemann-Liouville fractional integrals. The main edge of the newly established inequalities is that these can be turned into several new and existing inequalities for different fractional integrals like Riemann-Liouville fractional integrals, k-fractional integrals, Katugampola fractional operators, conformable fractional operators, Hadamard fractional operators, and fractional operators with the exponential kernel without proving one by one. It is also shown that the newly established inequalities are the refinements of the previously established inequalities inside the literature.http://dx.doi.org/10.1155/2022/6261970 |
| spellingShingle | Jarunee Soontharanon Muhammad Aamir Ali Hüseyin Budak Pinar Kösem Kamsing Nonlaopon Thanin Sitthiwirattham Some New Generalized Fractional Newton’s Type Inequalities for Convex Functions Journal of Function Spaces |
| title | Some New Generalized Fractional Newton’s Type Inequalities for Convex Functions |
| title_full | Some New Generalized Fractional Newton’s Type Inequalities for Convex Functions |
| title_fullStr | Some New Generalized Fractional Newton’s Type Inequalities for Convex Functions |
| title_full_unstemmed | Some New Generalized Fractional Newton’s Type Inequalities for Convex Functions |
| title_short | Some New Generalized Fractional Newton’s Type Inequalities for Convex Functions |
| title_sort | some new generalized fractional newton s type inequalities for convex functions |
| url | http://dx.doi.org/10.1155/2022/6261970 |
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