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 _{۱}\kappa _{۲}}{\mathcal{\varkappa }}\right)  is bounded. We also prove again a Hermite-Hadamard type inequality obtained in [۳۴] under the condition \phi ^{\prime }\left( \kappa_{۱}+\kappa _{۲}-\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.

کلیدواژه ها:

Hermite-Hadamard inequality ، convex function ، Bounded function