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Dal'nevost. Mat. Zh., 2010, Volume 10, Number 2, Pages 130–152 (Mi dvmg65)  

This article is cited in 2 scientific papers (total in 2 papers)

Some applications of extremal decompositions in the geometric function theory

V. N. Dubinin, D. A. Kirillova

Institute of Applied Mathematics, Far-Eastern Branch of the Russian Academy of Sciences

Abstract: The applications of the extremal decompositions of the domains and condensers in the geometric function theory are considered. We prove new theorems for the families of meromorphic functions without common values, the multipoint distortion theorems and the estimates of the coefficients for univalent functions. Also, we get some new inequalities for polynomials. All results are obtained by the unified method using the suitable properties of the extremal decompositions. Previously, these properties were established by capacity approach and symmetrization.

Key words: meromorphic functions, Schwarzian derivative, distortion theorems, estimates of the coefficients, polynomials, extremal decompositions, condenser capacity.

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Document Type: Article
UDC: 517.54
MSC: Primary 30C55; Secondary 30C85, 30C10
Received: 30.04.2010

Citation: V. N. Dubinin, D. A. Kirillova, “Some applications of extremal decompositions in the geometric function theory”, Dal'nevost. Mat. Zh., 10:2 (2010), 130–152

Citation in format AMSBIB
\Bibitem{DubKir10}
\by V.~N.~Dubinin, D.~A.~Kirillova
\paper Some applications of extremal decompositions in the geometric function theory
\jour Dal'nevost. Mat. Zh.
\yr 2010
\vol 10
\issue 2
\pages 130--152
\mathnet{http://mi.mathnet.ru/dvmg65}
\elib{http://elibrary.ru/item.asp?id=15484867}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. V. N. Dubinin, “Methods of geometric function theory in classical and modern problems for polynomials”, Russian Math. Surveys, 67:4 (2012), 599–684  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    2. V. N. Dubinin, “Geometric estimates for the Schwarzian derivative”, Russian Math. Surveys, 72:3 (2017), 479–511  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
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