关于一类解析函数

On a class of Analytic Functions

设C(λ ,β) (λ是复数 ,Reλ ≥ 0 ,β是实数 ,β<1)表示单位圆盘E ={z:｜z｜ <1}内满足条件Re{f′(z) +λzf″(z) } >β (z∈E)的解析函数f(z) =z+∑∞n =2anzn 构成的类 ,本文导出偏差定理 ,系数估计 ,卷积性质 ,以及类中某些函数部分和的一个性质 .

Let C(λ,β)(Reλ≥0,β<1) denote the class of functions f(z)=z+∑∞n=2a nz n which are analytic in the unit disc E={z:｜z｜<1} and satisfy the condition Re{f′(z)+λzf″(z)}>β (z∈E). The object of the present paper is to derive coefficient estimates,distortion theorems and convolution properties for the class C(λ,β).A property of the partial sums of certain functions in the class is also given.