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 Existence of Solutions to the System of Generalized Implicit Vector Quasivariational Inequality Problems | Hindawi Publishing Corporation Journal of Inequalities and Applications Volume 2009 Article ID 654370 7 pages doi 2009 654370 Research Article Existence of Solutions to the System of Generalized Implicit Vector Quasivariational Inequality Problems Zhi Lin College of Science Chongqing Jiaotong University Chongqing 400074 China Correspondence should be addressed to Zhi Lin linzhi7525@ Received 31 March 2009 Revised 30 July 2009 Accepted 3 September 2009 Recommended by Yeol Je Cho We study the system of generalized implicit vector quasivariational inequality problems and prove a new existence result of its solutions by Kakutani-Fan-Glicksberg s fixed points theorem. As a special case we also derive a new existence result of solutions to the generalized implicit vector quasivariational inequality problems. Copyright 2009 Zhi Lin. 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 The system of generalized implicit vector quasivariational inequality problems generalizes the generalized implicit vector quasivariational inequality problems and the latter had been studied in 1-3 . In this paper we study the system of generalized implicit vector quasivariational inequality problems and prove a new existence result of its solutions by Kakutani-Fan-Glicksberg s fixed points theorem. For other existence results with respect to the system of generalized implicit vector quasivariational inequality problems we refer the reader to 4-6 and references therein. Let I be an index set finite or infinite . For each i e I let Xi and Yi be two Hausdorff topological vector spaces Ki a nonempty subset of Xi and Ci a closed convex and pointed cone of Yi with int Ci 0 where int Ci denotes the interior of Ci. Denote that K Hjefij iKj K nieIKi K X Kị X nieIXi. For each x e K we can write x xi xq . For each
