Existence and Connectedness of Solutions for Generalized Vector Quasi-Equilibrium Problems

In this paper, we establish three existence theorems for strongly efficient solutions, weakly efficient solutions and efficient solutions of generalized vector quasi-equilibrium problems by using the Fan-KKM theorem and the scalarization method. Moreover, we investigate the connectedness of the sets of weakly efficient solutions and efficient solutions for generalized vector quasi-equilibrium problems and make a new attempt to establish the path connectedness of the set of weakly efficient solutions for generalized vector quasi-equilibrium problems.