On new general versions of Hermite–Hadamard type integral inequalities via fractional integral operators with Mittag-Leffler kernel
Abstract The main motivation of this study is to bring together the field of inequalities with fractional integral operators, which are the focus of attention among fractional integral operators with their features and frequency of use. For this purpose, after introducing some basic concepts, a new...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2021-11-01
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| Series: | Journal of Inequalities and Applications |
| Subjects: | |
| Online Access: | https://doi.org/10.1186/s13660-021-02721-9 |
| _version_ | 1818823351796236288 |
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| author | Havva Kavurmacı Önalan Ahmet Ocak Akdemir Merve Avcı Ardıç Dumitru Baleanu |
| author_facet | Havva Kavurmacı Önalan Ahmet Ocak Akdemir Merve Avcı Ardıç Dumitru Baleanu |
| author_sort | Havva Kavurmacı Önalan |
| collection | DOAJ |
| description | Abstract The main motivation of this study is to bring together the field of inequalities with fractional integral operators, which are the focus of attention among fractional integral operators with their features and frequency of use. For this purpose, after introducing some basic concepts, a new variant of Hermite–Hadamard (HH-) inequality is obtained for s-convex functions in the second sense. Then, an integral equation, which is important for the main findings, is proved. With the help of this integral equation that includes fractional integral operators with Mittag-Leffler kernel, many HH-type integral inequalities are derived for the functions whose absolute values of the second derivatives are s-convex and s-concave. Some classical inequalities and hypothesis conditions, such as Hölder’s inequality and Young’s inequality, are taken into account in the proof of the findings. |
| first_indexed | 2024-12-18T23:38:36Z |
| format | Article |
| id | doaj.art-6dfc3a3d5694456592b93b5d7c51fecc |
| institution | Directory Open Access Journal |
| issn | 1029-242X |
| language | English |
| last_indexed | 2024-12-18T23:38:36Z |
| publishDate | 2021-11-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of Inequalities and Applications |
| spelling | doaj.art-6dfc3a3d5694456592b93b5d7c51fecc2022-12-21T20:47:27ZengSpringerOpenJournal of Inequalities and Applications1029-242X2021-11-012021111610.1186/s13660-021-02721-9On new general versions of Hermite–Hadamard type integral inequalities via fractional integral operators with Mittag-Leffler kernelHavva Kavurmacı Önalan0Ahmet Ocak Akdemir1Merve Avcı Ardıç2Dumitru Baleanu3Department of Mathematics Education, Faculty of Education, Van Yüzüncü Yıl UniversityDepartment of Mathematics, Faculty of Science and Arts, Ağrı İbrahim Çeçen UniversityDepartment of Mathematics, Faculty of Science and Arts, Adıyaman UniversityDepartment of Mathematics, Cankaya UniversityAbstract The main motivation of this study is to bring together the field of inequalities with fractional integral operators, which are the focus of attention among fractional integral operators with their features and frequency of use. For this purpose, after introducing some basic concepts, a new variant of Hermite–Hadamard (HH-) inequality is obtained for s-convex functions in the second sense. Then, an integral equation, which is important for the main findings, is proved. With the help of this integral equation that includes fractional integral operators with Mittag-Leffler kernel, many HH-type integral inequalities are derived for the functions whose absolute values of the second derivatives are s-convex and s-concave. Some classical inequalities and hypothesis conditions, such as Hölder’s inequality and Young’s inequality, are taken into account in the proof of the findings.https://doi.org/10.1186/s13660-021-02721-9s-convex functionsHermite–Hadamard inequalityHölder inequalityAtangana–Baleanu integral operatorsNormalization functionEuler gamma function |
| spellingShingle | Havva Kavurmacı Önalan Ahmet Ocak Akdemir Merve Avcı Ardıç Dumitru Baleanu On new general versions of Hermite–Hadamard type integral inequalities via fractional integral operators with Mittag-Leffler kernel Journal of Inequalities and Applications s-convex functions Hermite–Hadamard inequality Hölder inequality Atangana–Baleanu integral operators Normalization function Euler gamma function |
| title | On new general versions of Hermite–Hadamard type integral inequalities via fractional integral operators with Mittag-Leffler kernel |
| title_full | On new general versions of Hermite–Hadamard type integral inequalities via fractional integral operators with Mittag-Leffler kernel |
| title_fullStr | On new general versions of Hermite–Hadamard type integral inequalities via fractional integral operators with Mittag-Leffler kernel |
| title_full_unstemmed | On new general versions of Hermite–Hadamard type integral inequalities via fractional integral operators with Mittag-Leffler kernel |
| title_short | On new general versions of Hermite–Hadamard type integral inequalities via fractional integral operators with Mittag-Leffler kernel |
| title_sort | on new general versions of hermite hadamard type integral inequalities via fractional integral operators with mittag leffler kernel |
| topic | s-convex functions Hermite–Hadamard inequality Hölder inequality Atangana–Baleanu integral operators Normalization function Euler gamma function |
| url | https://doi.org/10.1186/s13660-021-02721-9 |
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