Gap functions and existence of solutions for generalized vector quasivariational inequalities

Abstract

The gap functions for generalized vector quasivariational inequalities in Hausdorff topological vector spaces are introduced, then using Fan–Knaster–Kuratowski–Mazurkiewicz (FKKM) theorem, some existence theorems for a class of generalized vector quasivariational inequalities under suitable assumptions are established. The obtained results extend and unify corresponding results in the literature.