On new general versions of Hermite-Hadamard type integral inequalities via fractional integral operators with Mittag-Leffler kernel
| Autor: | Ahmet Ocak Akdemir, Dumitru Baleanu, Merve Avci Ardic, Havva Kavurmaci Önalan |
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| Přispěvatelé: | Belirlenecek |
| Jazyk: | angličtina |
| Rok vydání: | 2021 |
| Předmět: |
Pure mathematics
Hölder inequality Field (mathematics) Type (model theory) Euler gamma function Hadamard transform QA1-939 Normalization function Discrete Mathematics and Combinatorics Atangana-Baleanu integral operators Atangana–Baleanu integral operators Mathematics Second derivative Hermite polynomials Computer Science::Information Retrieval Applied Mathematics Approximations Incomplete beta function Integral equation Hermite–Hadamard inequality Holder inequality Kernel (algebra) s-convex functions Hermite-Hadamard inequality Focus (optics) Analysis Derivatives |
| Zdroj: | Journal of Inequalities and Applications, Vol 2021, Iss 1, Pp 1-16 (2021) |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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