概率度量空间中的一类压缩映像不动点定理

One Fixed Point Theorem for a Contractive Mapping in the Probability Metric Space

在概率度量空间中讨论了一类压缩映像的不动点的存在性及唯一性问题,构造出迭代序列研究了其逼近情况,并研究了不动点的邻域性质,得到了一个有关压缩映像的新的不动点定理。最后,所获得的结果被推广到了15种特殊的情形。

In this paper, the existence and uniqueness of the fixed point for a class of contractive mappings in probability metric spaces were discussed, and some new iterative sequences were constructed as well as the approximation of new iterative sequences were studied. After that the properties of the fixed point＇ s neighbor dormain were studied and a new fixed point theorem was obtained. Finally, the new results presented in this paper were applied to fifteen particular situations.