On integral functions with derivatives univalent in a circle

• Date: 1991
• Main Authors: Sheremeta , M. N., Шеремета , М. Н.
• Format: Article
• Language: Russian
• Published: Institute of Mathematics, NAS of Ukraine 1991
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/9622
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

It is proved that if the increasing sequence $n_p$  of natural numbers satisfies the condition $n_{p+1}/n_p→1 (p→\infty)$ and all derivatives $f^{(n_p)}$  of the analytic function $f$ in $D=\{z : |z | < 1\}$ are univalent in $D$, then $f$ is an entire function. At the same time, for each...