Certain Hermite–Hadamard type inequalities involving generalized fractional integral operators

Abstract

Raina (East Asian Math J 21(2):191–203, 2005) introduced a new fractional integral operator which is a generalization of Riemann–Liouville fractional integral. Agarwal et al. (Fasc Math 204:5–27, 2016) provided some Ostrowski type fractional integral inequalities. Chen (J Math Inequal 10(1):75–81, 2016) gave extension and refinement of the Hermite–Hadamard inequality for convex functions via Riemann–Liouville fractional integrals. Here, motivated by the above-mentioned works, we aim at establishing extension and refinement of the Hermite–Hadamard type inequalities for a function with certain conditions by using new fractional integral operators introduced by Raina and Agarwal et al. above. The inequalities presented here are also pointed out to include some known results, as their special cases.