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

Abstract: In this paper we prove the Hermite–Hadamard–Fejér inequalities for an -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 and which are naturally joined to the -convex function are given. Finally, applications on -logarithmic mean and mean of the order are obtained. [Copyright &y& Elsevier]