On Some New Extensions of Inequalities of Hermite-Hadamard Type for Generalized Fractional Integrals
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 obtain...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
University of Maragheh
2022-06-01
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| Series: | Sahand Communications in Mathematical Analysis |
| Subjects: | |
| Online Access: | https://scma.maragheh.ac.ir/article_252483_5c418ef6a00ed8e07a0b5e2b742f20c3.pdf |
| Summary: | 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. |
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| ISSN: | 2322-5807 2423-3900 |