On New Extensions of Hermite-Hadamard Inequalities for Generalized Fractional Integrals

In this paper, we establish some Trapezoid and Midpoint type inequalities for generalized fractional integrals by utilizing the functions whose second derivatives are bounded . We also give some new inequalities for k-Riemann-Liouville fractional integrals as special cases of our main results. We also obtain some Hermite-Hadamard type inequalities by using the condition f^{\prime }(a+b-x)\geq f^{\prime }(x) for all x\in \left[ a,\frac{a+b}{۲}\right] instead of convexity.

Keywords:

Hermite-Hadamard inequality , convex function , Bounded function