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具有缺项系数的几类解析函数族的性质
引用本文:彭志刚.具有缺项系数的几类解析函数族的性质[J].数学物理学报(A辑),2008,28(4):661-669.
作者姓名:彭志刚
作者单位:湖北大学数学与计算机科学学院,武汉430062
摘    要:S*表示所有在单位圆盘 D 内解析且满足条件 f(0)=f′ (0)-1=0的星形函数族, K 表示所有在 D内解析且满足条件 f(0)=f′ (0)-1=0 的凸函数族, P 表示所有在 D 内解析且满足条件p(0)=1, Rep(z)>0 的函数族. 设Pn={p(z): p(z)=1+anzn+an+1zn+1+…∈ P}, S*n={f (z): f(z)=z+anzn+an+1zn+1+…∈ S*}, Kn={f (z): f (z)=z+anzn+an+1zn+1+…∈ K}. LSn*={g(z)=ln f(z)/z, f ∈ Sn*}, 其中对数函数取使得ln1=0的那个单值解析分支. 该文研究了函数族Sn*, Kn和LSn*的性质, 找出了解析函数族LSn*的极值点与支撑点,并对S*n与Kn的极值点和支撑点作了一些探讨.

关 键 词:闭一致收敛拓扑  极值点  支撑点
收稿时间:2007-01-15
修稿时间:2008-05-15

The Properties of Several Classes of Analytic Functions with Missing Coefficients
Peng Zhigang.The Properties of Several Classes of Analytic Functions with Missing Coefficients[J].Acta Mathematica Scientia,2008,28(4):661-669.
Authors:Peng Zhigang
Institution:(College of Mathematics and Computer Science, Hubei University, Wuhan 430062)
Abstract:Let A be the class of functions, which are analytic in the unit disc D={z:|z|<1}, with f (0)=f′(0)-1=0. Let S* be the set of starlike functions, S*={f (z)∈A, Re zf′(z) / f(z)>0, z ∈ D}. Let K be the set of convex functions, K={f(z) ∈ A, Re(1+zf’’(z) / f ’(z)>0, z∈ D}. P denotes the class of functions p(z), which are analytic in D and satisfy p(0)=1, Rep(z)>0. Let Pn={p(z): p(z)=1+anzn+an+1zn+1+… ∈ P}, S*n={f (z): f(z)=z+anzn+an+1zn+1+… ∈ S*}, Kn={ f(z): f (z)=z+anzn+an+1zn+1+ … ∈K}. LSn*={g(z)=ln f(z) / z, f ∈ Sn*}, where the logarithmic function satisfy ln1=0. In this article the author investigated the properties of the classes S*n, Kn and LSn*. The author obstained the extreme points and support points of LSn*, and discussed the extreme points and support points of S*n and Kn.
Keywords:Topology of uniform convergencezz  Extreme pointzz  Support pointzz
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