University of MaraghehSahand Communications in Mathematical Analysis2322-580719220220601On Some New Extensions of Inequalities of Hermite-Hadamard Type for Generalized Fractional Integrals657925248310.22130/scma.2022.539417.992ENHuseyinBudakDepartment of Mathematics, Faculty of Science and Arts, Duzce
University, Duzce, Turkey.0000-0001-8843-955XCandanCan BilişikDepartment of Mathematics, Faculty of Science and Arts, Duzce
University, Duzce, Turkey.0000-0001-5649-284XMehmet ZekiSarikayaDepartment of Mathematics, Faculty of Science and Arts, Duzce
University, Duzce, Turkey.0000-0002-6165-9242Journal Article20210921In 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.https://scma.maragheh.ac.ir/article_252483_5c418ef6a00ed8e07a0b5e2b742f20c3.pdf