在這篇論文中,首先我們推廣Komiya的一致性定理(coincidence theorem),將定理中多值函數的凸值條件以非循環(acyclic)條件取代,同時將其運算子的"逆映射為開集合值"的條件以"有局部交集非空"的性質代替.其次,我們利用新的一致性定理去證明一些截面定理(section theorem)與極大極小定理(minimax theorem).

In this paper, we will establish a coincidence theorem, which generalizes a result of Komiya. Indeed, we replace the closed convex-valued condition in Komiya's theorem by the acyclic condition, and replace the operator that has "open lower sections" by the operator that has "local intersection property". Further, we base on this coincidence theorem to prove some section theorems and some minimax theorems.