設X是一個非空G-凸空間，Y是一個拓樸空間，F屬於G-KKM(X,Y)，H,T 是一個從X映到Y的多值函數。在某些假設條件之下，我們證得F與T的一些同值點定理。我們也證明了一些推廣型G-KKM定理，並利用這些推廣型G-KKM定理證明一些變分不等式的存在性定理。本文的結果推廣了許多學者的研究結果。

Let X be a nonempty G-convex, let Y be a topological space, let F belong to G-KKM(X,Y), and let H,T be set-valued mappings. In this paper, we establish some coincidence theorems of F and T under some assumptions. We also establish some generalized G-KKM theorems and apply these generalized G-KKM theorems to establish the existence theorems concerning variational inequalities. Our results generalize many other authors’ results (for example, see, [7,13,19,22]).

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