某些解析函数的性质

Properties of Certain Analytic Functions

导出类Q(k,α,β ,γ)中函数的一些有趣的性质 ,其中Q(k,α ,β,γ)表示单位圆盘E ={z:｜z｜<1 }内满足条件Reαf(z)z +βf′(z) >γ的解析函数f(z) =z+∑∞m =k+ 1amzm 的类 ,这里k是正整数 ,α与β是复数 ,Reβ≥ 0 ,β≠ 0 ,α +β与γ是实数 ,且 0≤γ <α +β .

Let Q(k,α,β,γ)denote the class of functions of the form f(z)=z+∑∞m=k+1a mz m which are analytic in the unit disc E=z:｜z｜<1 and satisfy the condition Re αf(z)z+βf′(z)>γ (z∈E) where k∈N,α∈C,β∈C, Re β≥0,β≠0,α+β∈R and 0≤γ<α+β.The object of the present paper is to derive some interesting properties of functions in the class Q(k,α,β,γ).