Journal of Inequalities and Applications
Volume 2008 (2008), Article ID 435719, 14 pages
doi:10.1155/2008/435719
Research Article

Painleve-Kuratowski Convergences for the Solution Sets of Set-Valued Weak Vector Variational Inequalities

Z. M. Fang,1 S. J. Li,1 and K. L. Teo2

1College of Mathematics and Science, Chongqing University, Chongqing, 400044, China
2Department of Mathematics and Statistics, Curtin University of Technology, P.O. Box U1987, Perth, WA 6845, Australia

Received 16 July 2008; Revised 11 November 2008; Accepted 10 December 2008

Academic Editor: Donal O'Regan

Copyright © 2008 Z. M. Fang 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.

Abstract

Painleve-Kuratowski convergence of the solution sets is investigated for the perturbed set-valued weak vector variational inequalities with a sequence of mappings converging continuously. The closedness and Painleve-Kuratowski upper convergence of the solution sets are obtained. We also obtain Painleve-Kuratowski upper convergence when the sequence of mappings converges graphically. By virtue of a sequence of gap functions and a key assumption, Painleve-Kuratowski lower convergence of the solution sets is established. Some examples are given for the illustration of our results.