关于推广的Cauchy积分定理的一个新证明

New Proof of Generalized Cauchy Integral Theorem

构造了在函数连续情况下的一个平均函数 ,证明了该平均函数的若干性质 .研究特定区域内的解析函数用其平均函数逼近时 ,通过将该区域化分为几个特殊部分 ,分别讨论了各部分解析函数与其平均函数之间的差异 。

In this paper,a new proof of generalized Cauchy integral theorem is given using average function.First,we construct an average function of a continuous function,and derive some properties of such average function.Then we study how an analytic function on some particular region is approximated by its average function.We divide this region into several different parts,and then study the difference between the analytic function and its average function in each part.By estimating the remainder,we reprove the generalized Cauchy integral theorem.