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Dal'nevostochnyi Matematicheskii Zhurnal, 2009, Volume 9, Number 1-2, Pages 140–149
(Mi dvmg25)
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This article is cited in 3 scientific papers (total in 3 papers)
Distortion theorems for univalent functions in multiply-connected domains
E. G. Prilepkina Institute of Applied Mathematics, Far-Eastern Branch of the Russian Academy of Sciences
Abstract:
The $n$-point distortion theorem for meromorphic and univalent functions in multiply-connected domains is proved. As the corollaries we derive the new estimates for Schwarzian derivatives in an annulus. Also,
we get the inequality for derivatives of conformal and univalent mappings of non-overlapping domains on the plane with radial slits similar the Lavrentev inequality. The main results are expressed in terms of Newmann function and capacity of generalized condencers are applied to prove theorems.
Key words:
meromorphic functions, univalent functions, distortion theorems, Schwarzian derivative, annulus, condensers capacity, Newmann function.
Received: 15.05.2009
Citation:
E. G. Prilepkina, “Distortion theorems for univalent functions in multiply-connected domains”, Dal'nevost. Mat. Zh., 9:1-2 (2009), 140–149
Linking options:
https://www.mathnet.ru/eng/dvmg25 https://www.mathnet.ru/eng/dvmg/v9/i1/p140
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Abstract page: | 403 | Full-text PDF : | 133 | References: | 60 | First page: | 1 |
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