我們使用鄭志中先生,黃永裕先生以及許惠貞小姐近期介紹的擴充性KKM映射及嚴格的KKM性質之概念去研究若T屬於SKKM(X,X)而X為拓樸向量空間$E$中的可行概凸子集的定點問題.我們建立若T屬於SKKM(X,X)是緊緻閉函數,則T就有定點.藉由這個新定點理論我們可以應用於某些遊戲理論中的平衡點問題.

　We use the concepts of generalized KKM mapping and the strict KKM property, which are recently introduced by J. C. Jeng, Y. Y. Huang and H. C. Hsu, to investigate the fixed point problem for T belong to SKKM(X,X) with X an admissible almost convex subset of a topological vector space E. We establish that if T belong to SKKM}(X,X) is compact and closed, then it has a fixed point. As applications of this new fixed point theorem, some results related to equilibrium problem in game theory are also deduced.

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