概率度量空间与映象的不动点定理

概率度量空间的概念首先由Menger7]提出,以后许多人对这一空间的理论和应用曾进行过某些讨论(见1-9])。本文的目的是进一步研究这一空间中映象的不动点定理。在本文的§2中,我们得出了一些新型的不动点定理,这些结果改进和加强了引文2,3,8]中某些主要结果。

Probabilistic Metric Spaces and Fixed Point Theorems for Mappings

Probabilistiic metric spaces were first studied by K. Menger7] in 1942 and further developed by him and several authors. For detailed discussions of probabitistic metric spaces and their applications we refer to 1]-9].In the present paper, we continue the study of fixed point theorems of mappings on probabilistic metric spaees. In §2 of this paper we obtain several new fixed point theorems which generalize some well-known results in Sehgal, Bharucha-Reid3] and Bocsan8]. In addition, we also utilize theorems of the type considered in §2 to study fixed point theorems of mappings on Wald spaces.