On Some New Extensions of Inequalities of Hermite-Hadamard Type for Generalized Fractional Integrals
| Autor: | Huseyin Budak, Candan Can Bilişik, Mehmet Sarikaya |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2022 |
| Předmět: | |
| Zdroj: | Sahand Communications in Mathematical Analysis, Vol 19, Iss 2, Pp 65-79 (2022) |
| Druh dokumentu: | article |
| ISSN: | 2322-5807 2423-3900 |
| DOI: | 10.22130/scma.2022.539417.992 |
| Popis: | In this paper, we establish some inequalities for generalized fractional integrals by utilizing the assumption that the second derivative of $\phi (x)=\varpi \left( \frac{\kappa _{1}\kappa _{2}}{\mathcal{\varkappa }}\right) $ is bounded. We also prove again a Hermite-Hadamard type inequality obtained in [34] under the condition $\phi ^{\prime }\left( \kappa_{1}+\kappa _{2}-\mathcal{\varkappa }\right) \geq \phi ^{\prime }(\mathcal{\varkappa })$ instead of harmonically convexity of $\varpi $. Moreover, some new inequalities for $k$-fractional integrals are given as special cases of main results. |
| Databáze: | Directory of Open Access Journals |
| Externí odkaz: |
|