HERMITE–HADAMARD TYPE INEQUALITIES FOR KATUGAMPOLA FRACTIONAL INTEGRALS

Abstract

In the paper, basing on the Katugampola fractional integrals ${}^\rho\mathcal{K}^\alpha_{a+}f$ and ${}^\rho\mathcal{K}^\alpha_{b-}f$ with $f\in\mathfrak{X}_c^p(a,b)$, the authors establish the Hermite-Hadamard type inequalities for convex functions, give their left estimates, and apply these newly-established inequalities to special means of real numbers. When $\rho\to1$, these results become the corresponding ones for the Riemann-Liouville fractional integrals.