Riemann–Liouville Fractional Newton’s Type Inequalities for Differentiable Convex Functions
In this paper, we prove some new Newton’s type inequalities for differentiable convex functions through the well-known Riemann–Liouville fractional integrals. Moreover, we prove some inequalities of Riemann–Liouville fractional Newton’s type for functions of bounded variation. It is also shown that...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-03-01
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| Series: | Fractal and Fractional |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2504-3110/6/3/175 |
| _version_ | 1797471525466537984 |
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| author | Thanin Sitthiwirattham Kamsing Nonlaopon Muhammad Aamir Ali Hüseyin Budak |
| author_facet | Thanin Sitthiwirattham Kamsing Nonlaopon Muhammad Aamir Ali Hüseyin Budak |
| author_sort | Thanin Sitthiwirattham |
| collection | DOAJ |
| description | In this paper, we prove some new Newton’s type inequalities for differentiable convex functions through the well-known Riemann–Liouville fractional integrals. Moreover, we prove some inequalities of Riemann–Liouville fractional Newton’s type for functions of bounded variation. It is also shown that the newly established inequalities are the extension of comparable inequalities inside the literature. Finally, we give some examples with graphs and show the validity of newly established inequalities. |
| first_indexed | 2024-03-09T19:49:25Z |
| format | Article |
| id | doaj.art-9950a9f679784f63adf179a8dabe483b |
| institution | Directory Open Access Journal |
| issn | 2504-3110 |
| language | English |
| last_indexed | 2024-03-09T19:49:25Z |
| publishDate | 2022-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj.art-9950a9f679784f63adf179a8dabe483b2023-11-24T01:14:55ZengMDPI AGFractal and Fractional2504-31102022-03-016317510.3390/fractalfract6030175Riemann–Liouville Fractional Newton’s Type Inequalities for Differentiable Convex FunctionsThanin Sitthiwirattham0Kamsing Nonlaopon1Muhammad Aamir Ali2Hüseyin Budak3Mathematics Department, Faculty of Science and Technology, Suan Dusit University, Bangkok 10300, ThailandDepartment of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, ThailandJiangsu Key Laboratory for NSLSCS, School of Mathematical Sciences, Nanjing Normal University, Nanjing 210023, ChinaDepartment of Mathematics, Faculty of Science and Arts, Düzce University, Düzce 81620, TurkeyIn this paper, we prove some new Newton’s type inequalities for differentiable convex functions through the well-known Riemann–Liouville fractional integrals. Moreover, we prove some inequalities of Riemann–Liouville fractional Newton’s type for functions of bounded variation. It is also shown that the newly established inequalities are the extension of comparable inequalities inside the literature. Finally, we give some examples with graphs and show the validity of newly established inequalities.https://www.mdpi.com/2504-3110/6/3/175Simpson's \({\frac{3}{8}}\) formulafractional calculusconvex functions |
| spellingShingle | Thanin Sitthiwirattham Kamsing Nonlaopon Muhammad Aamir Ali Hüseyin Budak Riemann–Liouville Fractional Newton’s Type Inequalities for Differentiable Convex Functions Fractal and Fractional Simpson's \({\frac{3}{8}}\) formula fractional calculus convex functions |
| title | Riemann–Liouville Fractional Newton’s Type Inequalities for Differentiable Convex Functions |
| title_full | Riemann–Liouville Fractional Newton’s Type Inequalities for Differentiable Convex Functions |
| title_fullStr | Riemann–Liouville Fractional Newton’s Type Inequalities for Differentiable Convex Functions |
| title_full_unstemmed | Riemann–Liouville Fractional Newton’s Type Inequalities for Differentiable Convex Functions |
| title_short | Riemann–Liouville Fractional Newton’s Type Inequalities for Differentiable Convex Functions |
| title_sort | riemann liouville fractional newton s type inequalities for differentiable convex functions |
| topic | Simpson's \({\frac{3}{8}}\) formula fractional calculus convex functions |
| url | https://www.mdpi.com/2504-3110/6/3/175 |
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