在本篇論文中，我們利用超凸度量空間的性質證明了可允許集的交集性質。利用這個性質，我們證得一些推廣型的變分不等式。我們也證明了四個實值函數，在某些假設條件之下的一些大中取小不等式的存在性定理。

In this paper, we use the property of hyperconvex metric space to establish an intersection property about a family of admissible sets. Applying this intersection property we establish some generalized variational inequality theorems. We also establish some minimax inequality theorems concerning four real-valued mappings under some assumptions.

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