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...
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2021
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oai:doaj.org-article:6dfc3a3d5694456592b93b5d7c51fecc2021-11-21T12:28:43ZOn new general versions of Hermite–Hadamard type integral inequalities via fractional integral operators with Mittag-Leffler kernel10.1186/s13660-021-02721-91029-242Xhttps://doaj.org/article/6dfc3a3d5694456592b93b5d7c51fecc2021-11-01T00:00:00Zhttps://doi.org/10.1186/s13660-021-02721-9https://doaj.org/toc/1029-242XAbstract 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.Havva Kavurmacı ÖnalanAhmet Ocak AkdemirMerve Avcı ArdıçDumitru BaleanuSpringerOpenarticles-convex functionsHermite–Hadamard inequalityHölder inequalityAtangana–Baleanu integral operatorsNormalization functionEuler gamma functionMathematicsQA1-939ENJournal of Inequalities and Applications, Vol 2021, Iss 1, Pp 1-16 (2021) |
| institution |
DOAJ |
| collection |
DOAJ |
| language |
EN |
| topic |
s-convex functions Hermite–Hadamard inequality Hölder inequality Atangana–Baleanu integral operators Normalization function Euler gamma function Mathematics QA1-939 |
| spellingShingle |
s-convex functions Hermite–Hadamard inequality Hölder inequality Atangana–Baleanu integral operators Normalization function Euler gamma function Mathematics QA1-939 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 |
| 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. |
| format |
article |
| 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 |
| title |
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_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_sort |
on new general versions of hermite–hadamard type integral inequalities via fractional integral operators with mittag-leffler kernel |
| publisher |
SpringerOpen |
| publishDate |
2021 |
| url |
https://doaj.org/article/6dfc3a3d5694456592b93b5d7c51fecc |
| work_keys_str_mv |
AT havvakavurmacıonalan onnewgeneralversionsofhermitehadamardtypeintegralinequalitiesviafractionalintegraloperatorswithmittaglefflerkernel AT ahmetocakakdemir onnewgeneralversionsofhermitehadamardtypeintegralinequalitiesviafractionalintegraloperatorswithmittaglefflerkernel AT merveavcıardıc onnewgeneralversionsofhermitehadamardtypeintegralinequalitiesviafractionalintegraloperatorswithmittaglefflerkernel AT dumitrubaleanu onnewgeneralversionsofhermitehadamardtypeintegralinequalitiesviafractionalintegraloperatorswithmittaglefflerkernel |
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1718419011612442624 |