Improved Hermite Hadamard type inequalities for harmonically convex functions via Katugampola fractional integrals

Abstract

In this paper,we proved three new Katugampola fractional Hermite- Hadamard type inequalities for harmonically convex functions by using the left and the right fractional integrals independently. One of our Katugampola frac- tional Hermite-Hadamard type inequalities is better than given in [15]. Also, we gave two new Katugampola fractional identities for differentiable functions. By using these identities, we obtained some new trapezoidal type inequalities for harmonically convex functions. Our results generalize many results from earlier papers.