這篇論文裡，我們首先把Himmelberg測量precompact集合的方法推廣到一般沒有線性結構的拓樸空間上，進而得到一個一般化的Metha’s Theorem，並應用此結果，對condensing mappings發展一些新的固定點定理。接著我們將建立一些新的極大元存在性及抽象經濟的平衡點存在性。針對兩類majorized的集值函數，我們改善了以前一些常見的存在性定理，並且將它一般化到l.c.-spaces上。

一種是對Lθ-majorized這類的集值函數，利用Tarafdar的固定點定理，在加入一個適當條件下，我們證明了一個common maximal element的存在性，並使用這個結果，推得一個抽象經濟的平衡點存在性；此外，也應用在求擬變分不等式的解。

另一種則是針對Φθ-majorized這類集值函數，我們先利用一個在H-space下已知的KKM principle去推得一個固定點定理，並用這個定理去推出我們想要的一些存在性結果。最後，我們也探討了模糊抽象經濟的平衡點存在性。

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