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

Abstract

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}{2}\right] $ instead of convexity.

Keywords

• hermite-hadamard inequality
• convex function
• bounded function