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Problemy Analiza — Issues of Analysis, 2017, Volume 6(24), Issue 1, Pages 58–67
DOI: https://doi.org/10.15393/j3.art.2017.3691
(Mi pa211)
 

Extension of starlike functions to a finitely punctured plane

D. V. Prokhorovab

a Petrozavodsk State University, 33, Lenina pr., Petrozavodsk 185910, Russia
b Saratov State University, 83, Astrakhanskaya st., Saratov 410012, Russia
References:
Abstract: We consider a sequence of functions which are starlike in the unit disk and their logarithmic derivatives are meromorphic with a finite number of simple poles in any boundary domain. These poles are either boundary deterministic or random with given characteristics. The aim of the article is the limit process and properties of the limit functions. We distinguish conditions for residues and distribution of poles. Under certain conditions, the sequence converges to the identity function. Another conditions allow us to obtain estimates for the limit function and its logarithmic derivative.
Keywords: starlike function, meromorphic function, weight, deterministic point regulation, uniform distribution.
Funding agency Grant number
Russian Science Foundation 17-11-01229
This work is supported by the Russian Science Foundation under grant 17-11-01229.
Received: 23.05.2017
Revised: 07.06.2017
Accepted: 10.06.2017
Bibliographic databases:
Document Type: Article
UDC: 517.5
MSC: 30C45, 60G55
Language: English
Citation: D. V. Prokhorov, “Extension of starlike functions to a finitely punctured plane”, Probl. Anal. Issues Anal., 6(24):1 (2017), 58–67
Citation in format AMSBIB
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\by D.~V.~Prokhorov
\paper Extension of starlike functions to a finitely punctured plane
\jour Probl. Anal. Issues Anal.
\yr 2017
\vol 6(24)
\issue 1
\pages 58--67
\mathnet{http://mi.mathnet.ru/pa211}
\crossref{https://doi.org/10.15393/j3.art.2017.3691}
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\elib{https://elibrary.ru/item.asp?id=29450649}
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