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.
"Existence Results for Nonsmooth Vector Quasi-Variational-Like Inequalities." Abstr. Appl. Anal. 2013 (SI45) 1 - 7, 2013. https://doi.org/10.1155/2013/376829