Some new classes of preinvex functions and directional variational-like inequalities

In this paper, we introduce and study some new classes of invex sets preinvex functions with respect to an arbitrary function k the bifunction ?(.,.); which are called generalized functions. These nonconvex include function, convex k-convex as special cases. We properties It is shown that minimum on can be characterized by a class variational inequalities, directional variational-like inequalities. Using auxiliary technique, several inertial type methods for solving inequalities proposed analyzed . Convergence analysis considered under suitable conditions. Some open problems also suggested future research.