Abstract
In this study, we define new classes of convexity called h-Godunova-Levin and h-Godunova-Levin preinvexity, through which some new inequalities of Hermite-Hadamard type are established. These new classes are the generalization of several known convexities including the s-convex, P-function, and Godunova-Levin. Further, the properties of the h-Godunova-Levin function are also discussed. Meanwhile, the applications of h-Godunova-Levin Preinvex function are given.