关于映象面积为有界的解析函数的几个问题(Ⅱ)

SOME PROBLEMS ON ANALYTIC FUNCTION WITH BOUNDED IMAGE BY THE MAPPING(Ⅱ)

本文是文[1]的继续,在本文中,我们首先改进了文[1]中的定理4,并证明了本文中,关于平均模的定理1与定理2。在文[2]中有如下关于|z|<R中,有界解析函数类的定理:设f(z)在|z|<R内解析,且|f(z)|<M,满足f(o)=o,|f′(o)|=a>o,那么W=f(z)的反函数在圆域|W|≤(aR)~z/6M内有单值解析的分支z=g(w),满足g(o)=o。本文将对S_m类函数进行研究,得到相应的两个定理。

Thie paper is the continuation of article (1). In this paper,firstly,theorem 4 in article (1) is improved and theorem 1 and theorem 2 concerning the mean modulus are proved. Then the anti-function of class SM is expounded and two results are obtained