| Weakly KKM Map, Intersection Theorems and Minimax Inequalities on Abstract Convex Spaces |
| Received:November 11, 2008 Revised:January 05, 2009 |
| Key Words:
abstract convex space map class ${\frak{K}}$ ${\frak{KC}}$ ${\frak{KO}}$ weakly KKM map matching theorem.
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| Fund Project:Supported by the National Natural Science Foundation of China (Grant No.10361005). |
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| Abstract: |
| In this paper, we introduce the concept of weakly KKM map on an abstract convex space without any topology and linear structure, and obtain Fan's matching theorem and intersection theorem under very weak assumptions on abstract convex spaces. Finally, we give several minimax inequality theorems as applications. These results generalize and improve many known results in recent literature. |
| Citation: |
| DOI:10.3770/j.issn:1000-341X.2010.06.019 |
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