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

Abstract

In this paper, we prove 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 fractional Hermite-Hadamard type inequalities is better than given in [17]. Also, we give two new Katugampola fractional identities for di¤erentiable functions. By using these identities, we obtain some new trapezoidal type inequalities for harmonically convex functions. Our results generalize many results from earlier papers.

Simpson Type Conformable Fractional Inequalities

“…The inequalities involving fractional integrals have become a noticeable approach in recent decades and have acted as a powerful tool for numerous investigations. In recent years, various types of new fractional integral inequalities including Hermite-Hadamard type inequalities have been established via convexity, which provides quite helpful and valid applications in areas such as probability theory, functional inequalities, interpolation spaces, Sobolev spaces, and information theory (see the papers [9,10]).…”