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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 |