sufficient conditions for the existence of solution for (ω − σ)-higher order strongly variational inequality

In this paper, a new version of a higher-order strongly convex function is introduced which is named (ω −σ)-higherorder strongly convex function. sufficient conditions for the existence of minimum for (ω − σ)-higher order strongly convex function is provided. the vector version of (ω − σ)-higher order strongly convex function is given and by using kkm theory an existence results for a solution of it is proved. moreover, the compactness of the solution set of the vector version of (ω − σ)-higher order strongly convex function is investigated. the results of this article improve and extend the corresponding results presented in this area.