Hermite–Hadamard type inequalities for F-convex function involving fractional integrals
Abstract In this study, the family F and F-convex function are given with its properties. In view of this, we establish some new inequalities of Hermite–Hadamard type for differentiable function. Moreover, we establish some trapezoid type inequalities for functions whose second derivatives in absolu...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2018-12-01
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| Series: | Journal of Inequalities and Applications |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1186/s13660-018-1950-1 |
| _version_ | 1818505006350860288 |
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| author | Pshtiwan Othman Mohammed Mehmet Zeki Sarikaya |
| author_facet | Pshtiwan Othman Mohammed Mehmet Zeki Sarikaya |
| author_sort | Pshtiwan Othman Mohammed |
| collection | DOAJ |
| description | Abstract In this study, the family F and F-convex function are given with its properties. In view of this, we establish some new inequalities of Hermite–Hadamard type for differentiable function. Moreover, we establish some trapezoid type inequalities for functions whose second derivatives in absolute values are F-convex. We also show that through the notion of F-convex we can find some new Hermite–Hadamard type and trapezoid type inequalities for the Riemann–Liouville fractional integrals and classical integrals. |
| first_indexed | 2024-12-10T21:44:56Z |
| format | Article |
| id | doaj.art-d0de04c9bd2b45409989fff7698da99e |
| institution | Directory Open Access Journal |
| issn | 1029-242X |
| language | English |
| last_indexed | 2024-12-10T21:44:56Z |
| publishDate | 2018-12-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of Inequalities and Applications |
| spelling | doaj.art-d0de04c9bd2b45409989fff7698da99e2022-12-22T01:32:23ZengSpringerOpenJournal of Inequalities and Applications1029-242X2018-12-012018113310.1186/s13660-018-1950-1Hermite–Hadamard type inequalities for F-convex function involving fractional integralsPshtiwan Othman Mohammed0Mehmet Zeki Sarikaya1Department of Mathematics, College of Education, University of SulaimaniDepartment of Mathematics, Faculty of Science and Arts, Düzce UniversityAbstract In this study, the family F and F-convex function are given with its properties. In view of this, we establish some new inequalities of Hermite–Hadamard type for differentiable function. Moreover, we establish some trapezoid type inequalities for functions whose second derivatives in absolute values are F-convex. We also show that through the notion of F-convex we can find some new Hermite–Hadamard type and trapezoid type inequalities for the Riemann–Liouville fractional integrals and classical integrals.http://link.springer.com/article/10.1186/s13660-018-1950-1F-convexλ φ $\lambda _{\varphi }$ -preinvexIntegral inequalities |
| spellingShingle | Pshtiwan Othman Mohammed Mehmet Zeki Sarikaya Hermite–Hadamard type inequalities for F-convex function involving fractional integrals Journal of Inequalities and Applications F-convex λ φ $\lambda _{\varphi }$ -preinvex Integral inequalities |
| title | Hermite–Hadamard type inequalities for F-convex function involving fractional integrals |
| title_full | Hermite–Hadamard type inequalities for F-convex function involving fractional integrals |
| title_fullStr | Hermite–Hadamard type inequalities for F-convex function involving fractional integrals |
| title_full_unstemmed | Hermite–Hadamard type inequalities for F-convex function involving fractional integrals |
| title_short | Hermite–Hadamard type inequalities for F-convex function involving fractional integrals |
| title_sort | hermite hadamard type inequalities for f convex function involving fractional integrals |
| topic | F-convex λ φ $\lambda _{\varphi }$ -preinvex Integral inequalities |
| url | http://link.springer.com/article/10.1186/s13660-018-1950-1 |
| work_keys_str_mv | AT pshtiwanothmanmohammed hermitehadamardtypeinequalitiesforfconvexfunctioninvolvingfractionalintegrals AT mehmetzekisarikaya hermitehadamardtypeinequalitiesforfconvexfunctioninvolvingfractionalintegrals |