压缩映像原理的简单应用——Banach空间等价范数与Lipschitz条件

Application of Contraction Mapping——Equivalent Norm in Banach Space and under Lipschitz Condition

观察Lipschitz条件与范数等价的命题在形式上的一致性,证明推导了结论:范数可以成为一个压缩映像,并利用这一思想来讨论范数一致收敛的问题.

For the similarity between Lipschitz condition and equivalent norm, a conclusion was given through proof and derivation, showing that the norm could be a contraction mapping. The problem of uniformed convergence of norm was discussed with the application of the conclusion.