Integral inequalities for some convex functions via generalized fractional integrals

Abstract

Abstract In this paper, we obtain the Hermite–Hadamard type inequalities for s-convex functions and m-convex functions via a generalized fractional integral, known as Katugampola fractional integral, which is the generalization of Riemann–Liouville fractional integral and Hadamard fractional integral. We show that through the Katugampola fractional integral we can find a Hermite–Hadamard inequality via the Riemann–Liouville fractional integral.

Keywords

• Hermite–Hadamard inequalities
• Riemann–Liouville fractional integral
• Hadamard fractional integral
• Katugampola fractional integral
• Convex functions
• s-convex functions