在這篇論文中，第一部分我們用到J.C.Jeng、H.C.Hsu和Y.Y.Hung所發表論文中的觀念，在超凸度量空間上定義廣義的 gKKM 函數以及 gKKM(X,Y) 集族，然而我們在 gKKM(X,Y) 集族上不需要緊緻條件就可以得到固定點定理。第二部分我們在 gKKM(X,Y)集族和Φ函數上證明了兩個大中取小不等式的定理。

In this work, we first use the conception of J. C. Jeng, H. C. Hsu and Y. Y. Huang [6] to define the generalized gKKM mapping and the class gKKM(X,Y) in hyperconvex metric spaces, and then we get a fixed point theorem on this family without compactness assumption. Next, we establish two minimax inequalities for the family gKKM(X,Y) and the Φ-mapping.

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