[[alternative]]Generalized Vector Quasi-Variational Inequalities On Nonconvex Constraint Regions

[[abstract]]We introduce a new class of nonconvex sets, which are named nearly convex set, and then extend several existence results on nonconvex optimization problems. In fact, the purpose of this paper is two fold: (1) we first obtain a rather general version of the G´orniewicz fixed point theorem by using the concept of generalized KKM mappings; (2) we establish some existence theorems for generalized vector quasi-variational inequality problems by applying our fixed point theorem. We derive several results here neither convex nor compact on constraint