Properties of harmonically-h-convex functions in connection to the Hermite-Hadamard-Fejér type inequalities

Abstract

The Hermite-Hadamard-Fejér inequalities for a harmonically-h-convex function are explored in this study, and the findings for specific classes of functions are highlighted. Several generalizations of the Hermite-Hadamard inequalities are also discussed. Some properties of functions H and F, which are naturally defined for Hermite-Hadamard-Fejér type inequalities for harmonically-h-convex functions, have also been studied. Finally, we find applications of the results concerning the p-logarithmic mean and the order p mean.