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.