某类星形函数的凸半径研究

STUDY ON THE CONVEX RADIUS ABOUT CERTAIN STAR FUNCTISNS

设ω(z)在单位圆盘D={z||z|<1}上单叶解析,且ω(0)=0,|ω(z)|<1,而p(z)=(1+Aω(z))/(1+Bω(z)),其中A,B满足条件:-1<B<0≤ A<1.记这些p(z)的全体为P(A,B)。另假设S*(A,B)={f(z)|f(z)在D上解析,且f(z)=z+a2z2+a3z3+……,zf'(z)/f(z)∈p(A,B)}[1]。本文将要给出的是关于S*(A,B)类函数在某特定条件下凸半径的求法。

That ω（z） is univalentlg analytic in the unite circular discD = {z｜｜z｜〈1} 〈 1},ω（0） =0,1 ω（z） ｜ 〈1 ,andwith-1 〈 B 〈 0 ≤A 〈 1 was supposed. The class of all thesep（z） asP（A,B） was denoted andS＇ （A,B） = {f（z） ｜f（z） is analytic in D and f（z） = z ＋ a2z^2 ＋ a3z^3 ＋ ,zf（z）/f（z） ∈ p（A ,B） }^[1]. The method for finding convex radius of the S^＊ （A ,B） functions under certain condition was presented.