dc.contributor.author |
Nasyrov S. |
|
dc.date.accessioned |
2018-09-18T20:00:57Z |
|
dc.date.available |
2018-09-18T20:00:57Z |
|
dc.date.issued |
2007 |
|
dc.identifier.issn |
0001-4346 |
|
dc.identifier.uri |
https://dspace.kpfu.ru/xmlui/handle/net/135762 |
|
dc.description.abstract |
We consider functions f that are univalent in a plane angular domain of angle απ, 0 < α ≤ 2. It is proved that there exists a natural number k depending only on α such that the kth derivatives f (k) of these functions cannot be univalent in this angle. We find the least of the possible values of for k. As a consequence, we obtain an answer to the question posed by Kir'yatskii: if f is univalent in the half-plane, then its fourth derivative cannot be univalent in this half-plane. © 2007 Pleiades Publishing, Ltd. |
|
dc.relation.ispartofseries |
Mathematical Notes |
|
dc.subject |
Bieberbach's conjecture |
|
dc.subject |
Holomorphic function |
|
dc.subject |
Koebe function |
|
dc.subject |
Univalent function |
|
dc.subject |
Weierstrass theorem |
|
dc.title |
On the univalence of derivatives of functions which are univalent in angular domains |
|
dc.type |
Article |
|
dc.relation.ispartofseries-issue |
5-6 |
|
dc.relation.ispartofseries-volume |
82 |
|
dc.collection |
Публикации сотрудников КФУ |
|
dc.relation.startpage |
798 |
|
dc.source.id |
SCOPUS00014346-2007-82-56-SID38349075342 |
|