Generalized Quasi-convex Vector-Valued Mapping and Minimax Inequalities

摘要

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.