扩张映射原理及其应用

Expansion mapping principle and its application

为了完善和发展不动点定理及其应用,本文给出扩张映射的概念,并利用Banach压缩映射原理证明扩张映射原理,进一步得到其他一些不动点定理。最后,详细论述扩张映射原理在证明方程解的存在性,求一些数列极限和判定函数是否有不动点定理的应用。

In order to improve and develop the fixed point theorem and its application,this paper gives the concept of expansion mapping,proves the principle by using Banach contraction mapping principle,and also gets some other fixed point theorems. Finally,the paper discusses whether the expansion mapping principle can be applied into the fixed point study on the existence of equation solution,seeking the limit of number series,and judging functions.