在本篇論文中，我們證明在超凸度量空間上的推廣型2-gKKM 定理。利用此定理，我們證得一些匹配定理、同值點定理及固定點定理。在應用方面，我們利用此推廣型2-gKKM 定理，證明一些變分不等式的存在性定理。

In this paper, we prove a generalized 2-gKKM theorem in hyperconvex metric space. By using this theorem we get a matching theorem, a coincidence theorem, and some fixed point theorems under some assumptions. As applications, we use this generalized 2-gKKM theorem to establish some existence theorems about variational inequalities.

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