摘要:本文介绍了常用的压缩映射、不动点定理的应用.在各类方程的求解问题里常转化为求映射的不动点，首先将原方程适当变形使其符合压缩映射原理的条件，以便应用逐次逼近法求得不动点即原方程的根.
关键词：压缩映射原理；不动点定理；逐次迭代法
ABSTRACT:This paper introduces some applications of Contraction mappings and the Banach Fixed-point theorem .Many kinds of equations can be transposed into fixed-point problems. The original equation is transformed so that the principle of contraction can be applied and a successive approximation method can be used to find the fixed-point, which is the solution to the equation.
Keywords: Contraction mapping principle; Fixed-point theorem; Method of successive iteration
本文中，我们在第一章对压缩映射及其相关概念作扼要的介绍；第二章中主要介绍压缩映射、不动点定理的应用，主要思想是把所求的方程通过转化，使其具有压缩映射的形式，再通过压缩映射的特点对其进行求解.在这里，我们所强调的是方程变形的手段，一些方程用通常的方法很难求出，但把它转化为具有压缩映射的条件以后就很容易求解了.
