弱压缩映射及其不动点定理

A Fixed Point Theorem on the Weak Contraction Mapping

本文首先引入弱压缩映射的概念,证明了几类常见的压缩映射都是弱压缩映射.最后给出弱压缩映射的不动点定理,从而说明弱压缩映射是具有一般性的压缩映射.

In this paper,the weak contraction mapping is defined.It is proved that several kinds of common contraction mapping are all weak contraction mapping.Finally,a fixed point theorem on the weak compacted mapping is given,thus the weak contraction mapping is general contraction mapping.