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 On Generalized Implicit Vector Equilibrium Problems in Topological Ordered Spaces | Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2009 Article ID 513408 9 pages doi 2009 513408 Research Article On Generalized Implicit Vector Equilibrium Problems in Topological Ordered Spaces Qun Luo Department of Mathematics Zhaoqing University Zhaoqing Guangdong 526061 China Correspondence should be addressed to Qun Luo liluoqun@ Received 4 June 2009 Revised 29 August 2009 Accepted 30 September 2009 Recommended by Nanjing Jing Huang We discuss three classes of generalized implicit vector equilibrium problems in topological ordered spaces. Under some conditions we prove three new existence theorems of solutions for the generalized implicit vector equilibrium problems in topological ordered spaces by using the Fan-Browder fixed point theorem. Copyright 2009 Qun Luo. 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 and Preliminaries It is well known that the vector equilibrium problem is closely related to vector variational inequality vector optimization problem and many others see . 1-6 and the references therein . Recently a large of generalized vector equilibrium problems have been studied in different conditions by many authors and a lot of results concerned with the existence of solutions and properties of solutions have been given in finite and infinite dimensional spaces see 7 and the references therein . The main purpose of this paper is to extend some known results for vector equilibrium problems to topological ordered spaces see 8 . We discuss three classes of generalized implicit vector equilibrium problems in topological ordered spaces. Under some conditions we prove three new existence theorems of solutions for the generalized implicit vector equilibrium problems in topological ordered spaces by using the Fan-Browder fixed .
