论文标题
有限分析功能的第三个导数的可变性区域
Variability regions for the third derivative of bounded analytic functions
论文作者
论文摘要
让$ z_0 $和$ w_0 $在打开单位磁盘$ \ mathbb {d} $中给出点，$ | w_0 | <| z_0 | $，和$ \ mathcal {h} _0 $是所有分析自我映射$ f $ of $ \ mathbb {d} $由$ f（0）= 0 $归一化的类。 In this paper, we establish the third order Dieudonné Lemma, and apply it to explicitly determine the variability region $\{f'''(z_0): f\in \mathcal{H}_0,f(z_0) =w_0, f'(z_0)=w_1\}$ for given $z_0,w_0,w_1$ and give the form of all the extremal functions.
Let $z_0$ and $w_0$ be given points in the open unit disk $\mathbb{D}$ with $|w_0| < |z_0|$, and $\mathcal{H}_0$ be the class of all analytic self-maps $f$ of $\mathbb{D}$ normalized by $f(0)=0$. In this paper, we establish the third order Dieudonné Lemma, and apply it to explicitly determine the variability region $\{f'''(z_0): f\in \mathcal{H}_0,f(z_0) =w_0, f'(z_0)=w_1\}$ for given $z_0,w_0,w_1$ and give the form of all the extremal functions.
