設X是一個非空集合，Y是一個非空FC空間，Z是一個拓樸空間，G屬於F-s-KKM(X,Y,Z)。在某些假設條件之下，我們證得G的一些同值點定理。我們也證明了一些推廣型F-s-KKM(X,Y,Z)定理，並利用這些推廣型F-s-KKM(X,Y,Z)定理證明一些推廣型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。

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