Extensions of Hermite–Hadamard inequalities for harmonically convex functions via generalized fractional integrals

Abstract

Abstract In the paper, the authors establish some new Hermite–Hadamard type inequalities for harmonically convex functions via generalized fractional integrals. Moreover, the authors prove extensions of the Hermite–Hadamard inequality for harmonically convex functions via generalized fractional integrals without using the harmonic convexity property for the functions. The results offered here are the refinements of the existing results for harmonically convex functions.

Keywords

• Harmonically convex functions
• Generalized fractional integrals
• Hermite–Hadamard inequalities