广义凸空间内的KKM型定理和极小极大不等式及鞍点定理  

KKM Type Theorems and Minimax Inequalities and Saddle Point Theorems in Generalized Convex Spaces

作　　者：丁协平[1] 

机构地区：[1]四川师范大学数学与软件科学学院,成都610066

出　　处：《数学学报（中文版）》2004年第4期711-722,共12页Acta Mathematica Sinica：Chinese Series

基　　金：国家自然科学基金(19871059);四川省教育厅重点研究基金

摘　　要：本文在非紧G-凸空间内对具有有限闭值和有限开值的G-KKM,广义G-KKM和广义S-KKM映象建立了某些新的KKM型定理。应用这些KKM型定理,在G-凸空间内得到了新的 Ky Fan型极小极大不等式和鞍点定理。这些结论推广了最近文献中的许多已有结果。In this paper, some new generalized KKM type theorems for G-KKM, gener- alized G-KKM and generalized S-KKM mappings with finitely closed values and with finitely open values are established in noncompact G-convex spaces. By using these KKM type theorems, some new Ky Fan type minimax inequalities and saddle poiat theorems are obtained in G-convex space. These results generalize a number of known results in the recent literature.

关 键 词：G-KKM型定理 极小极大不等式 鞍点 

分 类 号：O177.92[理学—数学] O189.11[理学—基础数学]