On the univalence of entire functions of bounded l-index |
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| Author |
m_m_sheremeta@list.ru
Ivan Franko National University of Lviv
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| 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 $\{ z:
|z-z_0|\leq\delta/l(|z_0|)\}.$
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| Keywords |
entire function; l-index boundedness; univalence
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| DOI |
doi:10.15330/ms.43.2.185-188
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| 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
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| Volume |
43
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| Issue |
1
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| Year |
2015
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| Journal |
Matematychni Studii
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| Full text of paper | |
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