运用压缩映射原理证明满足一定条件的函数存在定理及推广

压缩映射是度量空间与度量空间之间的一种特殊的对应关系,通过这种对应关系可以找到集合X中的稳定点即不动点;通过压缩映射定理知道满足一定条件的情况下可以得到唯一的不动点;在已有的定理证明上,通过一些条件的改变,然后得出新的命题,再用微分中值定理证明其正确性.

The Existence of Theorem and Generalization in Some Functions with Certain Condition Is Proved by Using Compression Mapping Principle

Compression mapping is a kind of special corresponding relation between metric spaces,the stability point in set X,fixed point,can be found through this kind of corresponding relation,as a result,we know that the only fixed point can be obtained under certain condition by compression mapping theorem,on the basis of the existed theorem proofs,by changing some conditions,new proposition is derived and then differential mean value theorem is used to prove its vallidity.