Generalized fractional Hadamard and Fejér-Hadamard inequalities for generalized harmonically convex functions (Q2221880)

Summary: In this paper, we define a new function, namely, harmonically \((\alpha,h-m)\)-convex function, which unifies various kinds of harmonically convex functions. Generalized versions of the Hadamard and the Fejér-Hadamard fractional integral inequalities for harmonically \((\alpha,h-m)\)-convex functions via generalized fractional integral operators are proved. From presented results, a series of fractional integral inequalities can be obtained for harmonically convex, harmonically \((h-m)\)-convex, harmonically \((\alpha,m)\)-convex, and related functions and for already known fractional integral operators.