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Báo cáo hóa học: " Research Article On Some Generalized Ky Fan Minimax Inequalities"

RTuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: esearch Article On Some Generalized Ky Fan Minimax Inequalities | Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2009 Article ID 194671 9 pages doi 10.1155 2009 194671 Research Article On Some Generalized Ky Fan Minimax Inequalities Xianqiang Luo Department of Mathematics Wuyi University Jangmen 529020 China Correspondence should be addressed to Xianqiang Luo luoxq1978@126.com Received 31 October 2008 Revised 26 March 2009 Accepted 21 April 2009 Recommended by Naseer Shahzad Some generalized Ky Fan minimax inequalities for vector-valued mappings are established by applying the classical Browder fixed point theorem and the Kakutani-Fan-Glicksberg fixed point theorem. Copyright 2009 Xianqiang 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 It is well known that Ky Fan minimax inequality 1 plays a very important role in various fields of mathematics such as variational inequality game theory mathematical economics fixed point theory control theory. Many authors have got some interesting achievements in generalization of the inequality in various ways. For example Ferro 2 obtained a minimax inequality by a separation theorem of convex sets. Tanaka 3 introduced some quasiconvex vector-valued mappings to discuss minimax inequality. Li and Wang 4 obtained a minimax inequality by using some scalarization functions. Tan 5 obtained a minimax inequality by the generalized G-KKM mapping. Verma 6 obtained a minimax inequality by an R-KKM mapping. Li and Chen 7 obtained a set-valued minimax inequality by a nonlinear separation function ịkrữ. Ding 8 9 obtained a minimax inequality by a generalized R-KKM mapping. Some other results can be found in 10-16 . In this paper we will establish some generalized Ky Fan minimax inequalities forvector-valued mappings by the classical Browder fixed point theorem and the Kakutani-Fan-Glicksberg fixed