论文标题
有限分析功能的第二个衍生物的可变性区域
Variability regions for the second 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 | $。令$ \ MATHCAL {H} _0 $为所有分析自动映射$ f $ $ \ mathbb {d} $由$ f（0）= 0 $和$ \ MATHCAL {H} _0（Z_0，W_0，W_0，W_0）= \ in \ in \ MathCAL {f \ Z___0 = k}在本文中，我们明确确定$ f'''（z_0）$的可变性区域时，$ f $范围超过$ \ mathcal {h} _0（z_0，w_0）$。我们还展示了Mathematica对我们主要结果的几何视图。
Let $z_0$ and $w_0$ be given points in the open unit disk $\mathbb{D}$ with $|w_0| < |z_0|$. Let $\mathcal{H}_0$ be the class of all analytic self-maps $f$ of $\mathbb{D}$ normalized by $f(0)=0$, and $\mathcal{H}_0 (z_0,w_0) = \{ f \in \mathcal{H}_0 : f(z_0) =w_0\}$. In this paper, we explicitly determine the variability region of $f''(z_0)$ when $f$ ranges over $\mathcal{H}_0 (z_0,w_0)$. We also show a geometric view of our main result by Mathematica.
