亚度量族生成空间的理论及其应用

Theory and applications for spanning spaces of meta-metric family

本文引进亚度量族生成空间的概念,Menger概率度量空间(E,F,△),当t-范数△满足,sup△(t,t)=1时,可视为亚度量族生成空间的特例。我们研究了亚度量族生成空间的拓扑结构,证明了这类空间中映象的几个不动点定理。作为其应用,给出了概率度量空间中相应的几个不动点定理。

In this paper, we introduce the concept of spanning spaces of meta-metric family and consider its topological structure. We prove somefixed point theorems of mappings in spanning spaces of meta-metricfamily. As their applications, we give corresponding some fixed pointtheorems in probabilistic metric spaces.