Conformable fractional Newton-type inequalities with respect to differentiable convex functions
Abstract The authors propose a new method of investigation of an integral identity according to conformable fractional operators. Moreover, some Newton-type inequalities are considered for differentiable convex functions by taking the modulus of the newly established equality. In addition, we prove...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2023-06-01
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| Series: | Journal of Inequalities and Applications |
| Subjects: | |
| Online Access: | https://doi.org/10.1186/s13660-023-02996-0 |
| _version_ | 1827922701232111616 |
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| author | Cihan Ünal Fatih Hezenci Hüseyin Budak |
| author_facet | Cihan Ünal Fatih Hezenci Hüseyin Budak |
| author_sort | Cihan Ünal |
| collection | DOAJ |
| description | Abstract The authors propose a new method of investigation of an integral identity according to conformable fractional operators. Moreover, some Newton-type inequalities are considered for differentiable convex functions by taking the modulus of the newly established equality. In addition, we prove several Newton-type inequalities with the aid of Hölder and power-mean inequalities. Furthermore, several new results are given by using special choices of the obtained inequalities. Finally, we give several inequalities of conformable fractional Newton-type for functions of bounded variation. |
| first_indexed | 2024-03-13T04:46:29Z |
| format | Article |
| id | doaj.art-6b6edd425e4b4571b9d2a89d1ab5554c |
| institution | Directory Open Access Journal |
| issn | 1029-242X |
| language | English |
| last_indexed | 2024-03-13T04:46:29Z |
| publishDate | 2023-06-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of Inequalities and Applications |
| spelling | doaj.art-6b6edd425e4b4571b9d2a89d1ab5554c2023-06-18T11:27:59ZengSpringerOpenJournal of Inequalities and Applications1029-242X2023-06-012023111910.1186/s13660-023-02996-0Conformable fractional Newton-type inequalities with respect to differentiable convex functionsCihan Ünal0Fatih Hezenci1Hüseyin Budak2Department of Mathematics, Faculty of Science and Arts, Sinop UniversityDepartment of Mathematics, Faculty of Science and Arts, Duzce UniversityDepartment of Mathematics, Faculty of Science and Arts, Duzce UniversityAbstract The authors propose a new method of investigation of an integral identity according to conformable fractional operators. Moreover, some Newton-type inequalities are considered for differentiable convex functions by taking the modulus of the newly established equality. In addition, we prove several Newton-type inequalities with the aid of Hölder and power-mean inequalities. Furthermore, several new results are given by using special choices of the obtained inequalities. Finally, we give several inequalities of conformable fractional Newton-type for functions of bounded variation.https://doi.org/10.1186/s13660-023-02996-0Newton formulaFractional calculusConformable fractional integrals |
| spellingShingle | Cihan Ünal Fatih Hezenci Hüseyin Budak Conformable fractional Newton-type inequalities with respect to differentiable convex functions Journal of Inequalities and Applications Newton formula Fractional calculus Conformable fractional integrals |
| title | Conformable fractional Newton-type inequalities with respect to differentiable convex functions |
| title_full | Conformable fractional Newton-type inequalities with respect to differentiable convex functions |
| title_fullStr | Conformable fractional Newton-type inequalities with respect to differentiable convex functions |
| title_full_unstemmed | Conformable fractional Newton-type inequalities with respect to differentiable convex functions |
| title_short | Conformable fractional Newton-type inequalities with respect to differentiable convex functions |
| title_sort | conformable fractional newton type inequalities with respect to differentiable convex functions |
| topic | Newton formula Fractional calculus Conformable fractional integrals |
| url | https://doi.org/10.1186/s13660-023-02996-0 |
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