Can I read Variability Regions for the Fourth Derivative of Bounded Analytic Functions on EtoBox?

Variability Regions for the Fourth Derivative of Bounded Analytic Functions by Chen, Gangqiang is a scholarly article available to read on EtoBox.

What is Variability Regions for the Fourth Derivative of Bounded Analytic Functions about?

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 fourth-order Dieudonn\'e's Lemma and apply it to determine the variability region $\{f^{(4)}(z_0): f\in \mathcal{H}_0,f(z_0) =w_0, f'(z_0)=w_1, f''(z_0)=w_2\}$ for given $z_0,w_0,w_1,w_2$ and give the form of all the extremal functions.

Author

Chen, Gangqiang

Published

2021

Language

EN