The aim of this paper is to study generalized vector quasi-equilibrium problems (GVQEPs) by scalarization method in locally convex topological vector spaces. A general nonlinear scalarization function for set-valued mappings is introduced, its main properties are established, and some results on the existence of solutions of the GVQEPs are shown by utilizing the introduced scalarization function. Finally, a vector variational inclusion problem is discussed as an application of the results of GVQEPs.
"Existence of Solutions for Generalized Vector Quasi-Equilibrium Problems by Scalarization Method with Applications." Abstr. Appl. Anal. 2013 1 - 8, 2013. https://doi.org/10.1155/2013/916089