关于两族特殊解析函数的邻域

Neighborhoods of Two classes of Special Analytic Functions

本文利用微分算子定义了两族解析函数,引入了它们的广义Ruschewey邻域,并研究了这两族解析函数与它们的邻域之间的关系。

Let the function f(z)=z+sum from n=2 to ∞ (a_nz^n) be analytic in |z|>1. For m∈N define D^mf=D(D^(m-1)f), D^of=f, D′f=zf′(z). We study the δ-neighborhoodN^m_δ(f)={h(z):h(z)=z+sum from n=2 to ∞ (b^nz^n), sum from n=2 to ∞ (n^m) |a_n-b_n|≤δ} of functions f(z) in the familiesC_α(m,p)={f: (D^mf(z))/(D^pg(z))>α, ReD^2g(z)>0, α>0, m≥p, |z|<1} and S~*(m, p)={f: (D^mf(z))/(D^pf(z))>0, m≥p, |z|<1}.Our results extend the corresponding theorems in [1], [2] and [3].