@article { author = {Budak, Huseyin and Can Bilişik, Candan and Sarikaya, Mehmet}, title = {On Some New Extensions of Inequalities of Hermite-Hadamard Type for Generalized Fractional Integrals}, journal = {Sahand Communications in Mathematical Analysis}, volume = {19}, number = {2}, pages = {65-79}, year = {2022}, publisher = {University of Maragheh}, issn = {2322-5807}, eissn = {2423-3900}, doi = {10.22130/scma.2022.539417.992}, abstract = {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.}, keywords = {Hermite-Hadamard inequality,convex function,Bounded function}, url = {https://scma.maragheh.ac.ir/article_252483.html}, eprint = {https://scma.maragheh.ac.ir/article_252483_5c418ef6a00ed8e07a0b5e2b742f20c3.pdf} }