# On the univalence of entire functions of bounded l-index

Author
Ivan Franko National University of Lviv
Abstract
For an entire function $f$ it is established a relation between the $l$-index boundedness of the derivative $f'$ and the existence for each $z_0\in \mathbb{C}$ of the derivative $f^{(k)}$ univalent in the disk $\{ z: |z-z_0|\leq\delta/l(|z_0|)\}.$
Keywords
entire function; l-index boundedness; univalence
DOI
doi:10.15330/ms.43.2.185-188
Reference
1. Kuzyk A.D., Sheremeta M.M. Entire functions of bounded l-index// DAN USSR, ser.A. – 1988. – ¹6. – P. 15–17. (in Ukrainian)

2. Sheremeta M.M. Analytic functions of bounded index. – Lviv: VNTL Publishers, 1999. – 141 p.

3. de Branges L. A proof of the Bieberbach conjecture// Acta Math. – 1985. – V.154, ¹1. – P. 137–152.

Pages
185-188
Volume
43
Issue
1
Year
2015
Journal
Matematychni Studii
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