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（School of Mathematics and Physics，Suzhou University of Science and Technology，Suzhou，Jiangsu 215009，China）

1 Introduction and Preliminaries

Lee［3］studied generalized KKM mapping and proved the following result：

In［5，6］，Park and Kim introduced and studied generalized convex spaces（simply，G-convex spaces）and obtained many important results in G-convex spaces.Since then，some authors［1，3，7］proved KKM theorems in G-convex spaces，which extended and improved the results of Park and Kim.

The purpose of this paper is to establish some new KKM theorems in G-convex spaces and，as applications，to obtain some new matching theorems and section theorem in G-convex spaces.The results presented in this paper improve and generalize the corresponding results in［2，3，7］.

2 New KKM Theorems

3 Matching Theorems

4 Section theorem

［1］Guo W P，Jung Im Kang and Yeol Je Cho.New KKM type theorems in G-convex spaces with applications［J］.J.Comput.Anal.Appl，2010，12（1－A）：100－110.

［2］Chen Y Q，Cho Y J，Kim J K，Lee B S.Note on KKM maps and applications［J］.Fixed Point Theory and Applications.Volume 2006.Article ID 53286，page 1－9doi：10.1155／FPTA／2006／53286.

［3］Lee W.Theory of generalized KKM maps on generalized convex spaces［J］.Ph.D Thesis，2001，1－79.

［4］Cho Y J，Kim J K，Lee B S.Remarks on KKM maps and applications［J］.Journal of Advanced Research in Applied Mathematics，2009，1：1－8.

［5］Park S，Kim H.Coincidence theorems for admissible multifunctions on generalized convex spaces［J］.J.Math.Anal.Appl，1996，197：173－187.

［6］Park S，Kim H.Foundations of the KKM theory on generalized convex spaces［J］.J.Math.Anal.Appl，1997，209：551－571.

［7］Park S.The KKM matching，and fixed point theorems in generalized convex spaces［J］.Nonlinear Funct.Anal.Appl，2006，11：139－154.