Generalized Quasi-convez Vector-Valued Mapping and Minimaz Inequalities
It is well known that Ky Fan minimax inequality plays a very important role in various fields of mathematics, such as variational inequality, game theory, mathematical economics, fixed point theory, control theory and so on. Many authors have got some interesting achievements in generalization of the inequality in various ways. For example. Ferro obtained a minimax inequality by a separation theoreM of convex sets. Tanaka introduced some quasiconvex vector-valued mappings to discuss minimax inequality. Li and Wang obtained a minimax inequality by using some scalarization functions. Tan obtained a minimax inequality by the generalized G-KKM mapping. Verma obtained a minimax inequality by an RKKM mapping. Li and Chen obtained a set-valued minimax inequality by a nonlinear separation function ξ k.s. Ding obtained a minimax inequality by a generalized R-KKMmapping. In this paper, we introduce a generalized quasi-convex vector-valued mapping and consider a KKM lemma. And by applying the KKM lemma, we establish some generalized minimax inequalities for vector-valued mapping which improve some previous results.
generalized quasi-convez mapping minimaz inequality, vector-valued mapping, generalized KKM mapping
Xianqiang Luo
Department of Mathematics, Wuyi University, Jangmen 529020, P.R. China
国际会议
The First World Congress on Global Optimization in Engineering & Science(第一届工程与科学全局优化国际会议 WCGO2009)
长沙
英文
749-753
2009-06-01（万方平台首次上网日期，不代表论文的发表时间）