本文證明一個在FC空間上的弱F-S-KKM推廣型函數的交集定理，利用這個定理證明了一些大中取小不等式的存在性定理。

In this paper, we establish an intersection theorem of a weakly F-S-KKM mapping in FC-space. Apply this theorem, we get an existence theorem concerning generalized minimax inequalities. These results generalized many known results from the literature.

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