@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}
}