Further generalizations of Hadamard and Fejér–Hadamard fractional inequalities and error estimates
Abstract The aim of this paper is to generalize the fractional Hadamard and Fejér–Hadamard inequalities. By using a generalized fractional integral operator containing extended Mittag-Leffler function via monotone function, for convex functions we generalize well known fractional Hadamard and Fejér–...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2020-08-01
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| Series: | Advances in Difference Equations |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1186/s13662-020-02872-x |
| _version_ | 1818517637203755008 |
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| author | Yongsheng Rao Muhammad Yussouf Ghulam Farid Josip Pečarić Iskander Tlili |
| author_facet | Yongsheng Rao Muhammad Yussouf Ghulam Farid Josip Pečarić Iskander Tlili |
| author_sort | Yongsheng Rao |
| collection | DOAJ |
| description | Abstract The aim of this paper is to generalize the fractional Hadamard and Fejér–Hadamard inequalities. By using a generalized fractional integral operator containing extended Mittag-Leffler function via monotone function, for convex functions we generalize well known fractional Hadamard and Fejér–Hadamard inequalities. Also we study the error bounds of these generalized Hadamard and Fejér–Hadamard inequalities. We also obtain some published results from presented inequalities. |
| first_indexed | 2024-12-11T00:58:56Z |
| format | Article |
| id | doaj.art-57eccf5b54ba4b399276a2b3abe1f657 |
| institution | Directory Open Access Journal |
| issn | 1687-1847 |
| language | English |
| last_indexed | 2024-12-11T00:58:56Z |
| publishDate | 2020-08-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Advances in Difference Equations |
| spelling | doaj.art-57eccf5b54ba4b399276a2b3abe1f6572022-12-22T01:26:23ZengSpringerOpenAdvances in Difference Equations1687-18472020-08-012020111410.1186/s13662-020-02872-xFurther generalizations of Hadamard and Fejér–Hadamard fractional inequalities and error estimatesYongsheng Rao0Muhammad Yussouf1Ghulam Farid2Josip Pečarić3Iskander Tlili4Institute of Computing Science and Technology, Guangzhou UniversityDepartment of Mathematics, University of SargodhaDepartment of Mathematics, COMSATS University IslamabadRudn UniversityDepartment of Management of Science and Technology Development, Ton Duc Thang UniversityAbstract The aim of this paper is to generalize the fractional Hadamard and Fejér–Hadamard inequalities. By using a generalized fractional integral operator containing extended Mittag-Leffler function via monotone function, for convex functions we generalize well known fractional Hadamard and Fejér–Hadamard inequalities. Also we study the error bounds of these generalized Hadamard and Fejér–Hadamard inequalities. We also obtain some published results from presented inequalities.http://link.springer.com/article/10.1186/s13662-020-02872-xConvex functionsHadamard inequalityGeneralized fractional integralsMittag-Leffler function |
| spellingShingle | Yongsheng Rao Muhammad Yussouf Ghulam Farid Josip Pečarić Iskander Tlili Further generalizations of Hadamard and Fejér–Hadamard fractional inequalities and error estimates Advances in Difference Equations Convex functions Hadamard inequality Generalized fractional integrals Mittag-Leffler function |
| title | Further generalizations of Hadamard and Fejér–Hadamard fractional inequalities and error estimates |
| title_full | Further generalizations of Hadamard and Fejér–Hadamard fractional inequalities and error estimates |
| title_fullStr | Further generalizations of Hadamard and Fejér–Hadamard fractional inequalities and error estimates |
| title_full_unstemmed | Further generalizations of Hadamard and Fejér–Hadamard fractional inequalities and error estimates |
| title_short | Further generalizations of Hadamard and Fejér–Hadamard fractional inequalities and error estimates |
| title_sort | further generalizations of hadamard and fejer hadamard fractional inequalities and error estimates |
| topic | Convex functions Hadamard inequality Generalized fractional integrals Mittag-Leffler function |
| url | http://link.springer.com/article/10.1186/s13662-020-02872-x |
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