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    (\omega-\sigma)-higher-order strongly convex function. Sufficient conditions for the existence of minimum for  (\omega-\sigma)-higher order strongly convex function is provided. The vector version of (\omega-\sigma)-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 (\omega-\sigma)-higher order strongly convex function is investigated. The results of this article improve and extend the corresponding results presented in this area.

کلیدواژه ها:

(ω − σ)- higher order convex function ، higher order variational inequalities ، KKM Theory