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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
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.
Received: 23.05.2017 Revised: 07.06.2017 Accepted: 10.06.2017
Citation:
D. V. Prokhorov, “Extension of starlike functions to a finitely punctured plane”, Probl. Anal. Issues Anal., 6(24):1 (2017), 58–67
Linking options:
https://www.mathnet.ru/eng/pa211 https://www.mathnet.ru/eng/pa/v24/i1/p58
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Abstract page: | 181 | Full-text PDF : | 60 | References: | 34 |
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