概率度量空间中的变分原理(Ⅰ)

A Variational Principle in Probabilistic Metric Spaces~*(Ⅰ)

本文研究概率度量空间中的变分原理。我们证明了概率分析中的一个序原理;应用这个序原理并引入分布值映射的下半连续性概念,把Ekeland变分原理和Caristi不动点定理推广到概率度量空间中。

We establish an ordering principle in probabilistic analysis,and by this ordering principle we show a variational principle in probabilistic metric spaces. This variational principle is a probabilistic generalization of Ekeland's variational principle. Using the probabilistic variational principle we show a fixed point theorem,which includes Caristi's fixed point theorem as a special case.