关于两类算子的研究

Two Kinds of Operators

本文给出了用算子Dλf(z)=z(1-z)λ+1*f(z)判别函数为单叶函数的两条判别法则,其中f(z)=z+∑∞k=2akzk,实数λ>-1,符号*为Hadamard卷积,并讨论了两类算子Dλ与Dn间的关系,这里算子Dn定义为D0f(z)=f(z),D1f(z)=Df(z)=zf′(z),Dnf(z)=D(Dn-1f(z)),n∈N.

This paper demonstrate two discriminant rules of functions being univalent, with operatorf（z）=z＋x∞∑k=2akzk,where Dλf（z）=z/（1-z）λ＋1＊f（z）real number λ 〉 - 1, the symbol ＊ refers to convolution. This paper also discusses the relations between two kinds of operators Dλ and Dn, and here Dn is defined as D0f（z）=f（z）=Df（z）=zf＇（z）,Dnf（z）=D（Dn-1f（z））,n∈N.