Existence results for nonsmooth vector quasi-variational-like inequalities
Summary: 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 the Fan-KKM theorem and a maximal element theorem. By using the technique and methodology adopted in [\textit{S. Al-Homidan} et al., in: Q. H. Ansari (ed.) et al., Recent developments in vector optimization. Berlin: Springer. Vector Optimization, 221--274 (2012; Zbl 1274.90333)] one can easily derive the relations between 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.
nonsmooth vector quasi-variational-like inequalities
scientific article; zbMATH DE number 6306707
scientific article