Existence Results for Nonsmooth Vector Quasi-Variational-Like Inequalities

الملخص EN

We introduce nonsmooth vector quasi-variational-like inequalities (NVQVLI) by means of a bifunction.

We establish some existence results for solutions of these inequalities by using Fan-KKM theorem and a maximal element theorem.

By using the technique and methodology adopted in Al-Homidan et al.

(2012), one can easily derive the relations among these inequalities and a vector quasi-optimization problem.

Hence, the existence results for a solution of a vector quasi-optimization problem can be derived by using our results.

The results of this paper extend several known results in the literature.