Inequalities for complex rational functions

• Date: 2021
• Main Authors: Bidkham, M., Khojastehnezhad, E.
• Format: Article
• Language: English
• Published: Institute of Mathematics, NAS of Ukraine 2021
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/455
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

UDC 517.5 For the rational function $r(z)=p(z)/H(z)$ having all its zeros in $|z|\leq 1,$ it is known that\begin{equation*}|r'(z)|\geq\dfrac{1}{2}|B'(z)||r(z)|\quad \text{for}\quad |z|=1,\end{equation*}where $H(z)=\prod_{j=1}^n(z - c_j),$ $|c_j|>1,$ $n$ is a positive int...