Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article Painleve-Kuratowski Convergences for the Solution Sets of Set-Valued Weak Vector Variational Inequalities | Hindawi Publishing Corporation Journal of Inequalities and Applications Volume 2008 Article ID 435719 14 pages doi 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 1 College of Mathematics and Science Chongqing University Chongqing 400044 China 2 Department of Mathematics and Statistics Curtin University of Technology . Box U1987 Perth WA 6845 Australia Correspondence should be addressed to S. J. Li lisj@ Received 16 July 2008 Revised 11 November 2008 Accepted 10 December 2008 Recommended by Donal O Regan 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. 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. 1. Introduction Since the concept of vector variational inequality VVI was introduced by Giannessi 1 in 1980 many important results on various kinds of vector variational inequality problems have been established such as existence of solutions relations with vector optimization stability of solution set maps gap function and duality theories see . 2-8 and the references cited therein . The stability analysis of the solution set maps for the parametric VVI problem is of considerable interest amongst .
