Properties of hh-convex functions related to the Hermite–Hadamard–Fejér inequalities

In this paper we prove the Hermite–Hadamard–Fejér inequalities for an hh-convex function and we point out the results for some special classes of functions. Also, some generalization of the Hermite–Hadamard inequalities and some properties of functions HH and FF which are naturally joined to the hh-convex function are given. Finally, applications on pp-logarithmic mean and mean of the order pp are obtained.