Abstract and Applied Analysis
Volume 2013 (2013), Article ID 916089, 8 pages
http://dx.doi.org/10.1155/2013/916089
Research Article

Existence of Solutions for Generalized Vector Quasi-Equilibrium Problems by Scalarization Method with Applications

De-ning Qu1,2 and Cao-zong Cheng1

1College of Applied Science, Beijing University of Technology, Beijing 100124, China
2College of Mathematics, Jilin Normal University, Siping, Jilin 136000, China

Received 26 November 2012; Accepted 6 February 2013

Academic Editor: Ngai-Ching Wong

Copyright © 2013 De-ning Qu and Cao-zong Cheng. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

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.