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Problemy Analiza — Issues of Analysis, 2014, Volume 3(21), Issue 2, Pages 59–73
DOI: https://doi.org/10.15393/j3.art.2014.2729 (Mi pa183) 		 
This article is cited in 10 scientific papers (total in 10 papers)

Univalence of harmonic functions, problem of Ponnusamy and Sairam, and constructions of univalent polynomials

V. V. Starkov

Petrozavodsk State University, Lenin Avenue, 33, 185910 Petrozavodsk, Russia
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DOI: https://doi.org/10.15393/j3.art.2014.2729
Abstract: The criteria of the univalence of a harmonic mapping is obtained in this paper. Particularly, it permits to formulate the hypothesis of the harmonic function classes equality $S_H^0=S_H^0(S)$ (hypothesis of Ponnusamy and Sairam), in analytic form. The method of construction of the univalent harmonic polynomials with desired properties, according to a given harmonic function, is obtained by means of the univalence criteria.
Keywords: harmonic functions, criteria of the univalence, harmonic univalent polynomials.
Received: 07.09.2014
Bibliographic databases:
Document Type: Article
MSC: 30C55, 30C10, 31A05
Language: English
Citation: V. V. Starkov, “Univalence of harmonic functions, problem of Ponnusamy and Sairam, and constructions of univalent polynomials”, Probl. Anal. Issues Anal., 3(21):2 (2014), 59–73
Citation in format AMSBIB
\Bibitem{Sta14}
\by V.~V.~Starkov
\paper Univalence of harmonic functions, problem of Ponnusamy and Sairam, and constructions of univalent polynomials
\jour Probl. Anal. Issues Anal.
\yr 2014
\vol 3(21)
\issue 2
\pages 59--73
\mathnet{http://mi.mathnet.ru/pa183}
\crossref{https://doi.org/10.15393/j3.art.2014.2729}
\elib{https://elibrary.ru/item.asp?id=22927223}
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    • This publication is cited in the following 10 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Problemy Analiza — Issues of Analysis
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