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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 492103, 4 pages
Research Article

A Note on Scalar-Valued Gap Functions for Generalized Vector Variational Inequalities

1College of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing 400067, China
2College of Automation, Chongqing University, Chongqing 400030, China
3School of Management, Southwest University of Political Science and Law, Chongqing 401120, China

Received 1 November 2013; Accepted 17 December 2013

Academic Editor: Khalil Ezzinbi

Copyright © 2013 Xiang-Kai Sun et al. 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.


This paper is concerned with gap functions of generalized vector variational inequalities (GVVI). By using scalarization approach, scalar-valued variational inequalities of (GVVI) are introduced. Some relationships between the solutions of (GVVI) and its scalarized versions are established. Then, by using these relationships and some mild conditions, scalar-valued gap functions for (GVVI) are established.