Bazilevich函数及其导数的一类α阶组合

Combinations of Order a of Bazilevich Functions and its Derivatives

设Ｆ（ｚ）＝ｚ＋Ａ＿（ｎ＋１）ｚ￣（ｎ＋１）＋…，是单位圆内的一种Ｂａｚｉｌｅｖｉｃｈ函数．考察由组合式（ｆ（ｚ）／ｚ）￣ａ＝（Ｆ（ｚ）定义的ｆ（ｚ）的性质，其中ａ＞０，证明了仍然在Ｆ（ｚ）所在的族中，其中Ｒ＿０＜１是一个二次方程的正根。

et Fz)=z+A￣(n+1)+…be analytic in the unit disc U={x:|z|<1}。B_n(α,ρ)denotes a family of Bazilevich functions such that F(z)∈B_n(α,ρ)if and only if there exists a function G(z)=z+C_(n+1)z￣(n+1)+…,,o≤ρ<1,α>0 withRe where S*ρ denotes the class of starlike functions of order ρ. let F(z)∈B_n(α,),0≤ρ<1,a>0,and f (z)be defined by relationthen it is proved in this paper that satisfies,where R_0 is the positive root of the equation