关于“一族特殊的星像函数”一文的补充

<正> 1.作者在前一文中证明了下面的结果:1°设 f(z)=z+a_z~2+…在单位圆|z|<1中满足条件(?)就是说 f(z)属于函数族 S,那末 f(z)的任何开始多项式σ_n(z)=z+…+a_nZ~n都在圆|z|<1/2中是单叶的.

A CLASS OF FUNCTIONS WITH STARSHAPED IMAGES

Let S be the class of functionssatisfying the con-dition.In my previous paper,it is proved that:if f(z)∈ S,then any section σ_n(z)=z+…+α_nz~n(n≥2)of f(z)is star-shaped in the circle |z|<1/2,unless n=3,4,5;and that 3σ_n(1/3z)∈Sunless n=3.In this note,I have pointed out that the above results hold good evenwhen n=3.