一类解析函数的星形半径

The Radius of Starlikeness of Certain Analytic Functions

令f(z)=z+∑∞n=2anzn∈S,g(z)=11+cz1-c[zcf(z)]′=∑∞n=1n+c1+canzn(c=1,2,…),Sn(z,g)=∑nk=1k+c1+cakzk,本文证明了当c=2时一切Sn(z,g)在|z|<316内星形且星形半径最好。

let f（z）=z＋∞∑（n=2）anz^n∈S,g（z）=1/（1＋c）z^1-c[z^cf（z）]′=∞∑（n=1）n＋c/1＋canz^n（c=1,2,…）,Sn（z,g）=n∑（k=1）k＋c/1＋cakz^k,This paper proves that all the Sn（z,g） will be starlike functions in the domain ｜z｜〈3/16 when c = 2, and the best radius is 3/16.