概率区间空间中的新型KKM定理及应用

New Version of KKM Theorem in Prohahilistic Metric Spaces with Applications

本文建立了概率区间空间的概念，并在此框架下建立了一个新型的ＫＫＭ定理．作为应用我们得到了概率区间空间中的一个新的极大极小定理和截口定理，匹配定理及一些重合点定理．所得结果均是全新的，它们不仅包含了ＶｏｍＮｅｕｍａｎｎ［７］中的主要结果，而且将［１］［３～４］［６］，［８］中的相应结果推广到概率区间空间。

In this paper we first introduce the concept of probabilistic interval space.Under this framework. a new version of KKM theorem is obtained. As applications, we utilize this result to study some new minimz.x theorem, section theorem,matching theorem, coincidence theorem, and fixed point theorem in probabilisticmetric spaces. The results presented in this paper not only contain the mainresult of von Neumann [7] as its spacial case but also extend the correspondingresults of [1, 3, 4, 6, 8] to the case of probabilistic metric spa'ces.