全纯函数和整函数的正规族

Normal Families of Holomorphic Functions and Entire Functions

在全纯函数及整函数上讨论了 {f(z) }和 {f(f(z) ) }的正规族之间的关系 ,得到关于全纯函数及整函数族的一些正规定则 :设F ={f(z) }是整函数族 ,记p(z) =f[f(z) ],若在单位圆盘Δ内 ,f(z)≠ 0 ,当p′(z) =a≠ 0时 ,|p(z) |=|f[f(z) ]|≥h >0 ;或 f(z)∈F ,|f(0 ) |<1,当p′(z) =a≠ 0时 ,|p(z) |≥h1>0 ;且当p(z) =0时 ,|p′(z) |≤h2 (>0 ) ,则F在Δ上正规。最后给出了其应用。

In this paper,the author discusses the relation of normalities between { f(z )} and { f(f(z)) },and obtains some normal criteria of the family of holomorphic functions and entire functions.Let F={f(z)} b a family of entire functions, p(z)=f , f(z) ≠0,| p(z )|≥ h >0,whenever p′(z )= a ≠0,or  f(z )∈ F ,| f (0)|<1,| p(z )|≥ h 1>0,whenever p′(z)=a ≠0;| p′(z )|≤ h 2(>0),whenever p(z) =0,then F is normal in then unit disc Δ.