Journal of Inequalities and Applications
Volume 2008 (2008), Article ID 435719, 14 pages
Painleve-Kuratowski Convergences for the Solution Sets of Set-Valued Weak Vector Variational Inequalities
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.
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.