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Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, 2014, Volume 156, Book 1, Pages 31–43 (Mi uzku1227)  

This article is cited in 10 scientific papers (total in 10 papers)

On the exit out of the Gakhov set controlled by the subordination conditions

A. V. Kazantsev

Institute of Computer Mathematics and Information Technologies, Kazan (Volga Region) Federal University, Kazan, Russia
References:
Abstract: A Gakhov set $\mathcal G$ is the class of all holomorphic and locally univalent functions in the unit disk, which have no more than one root of the Gakhov equation. For the series of the well-known subclasses of univalent functions having the zero root of the Gakhov equation, an effective desription is given for the set of all trajectories of the exit out of $\mathcal G$; such an exit takes place when the parameter value corresponds to the sharp constant in the appropriate uniqueness condition of the root. It is shown that the exit out of $\mathcal G$ may occur due to the bifurcations of the two following types only: 1) the maximum at zero splits into two maxima and the saddle; 2) the non-zero semisaddle appears and then divides into the maximum and the saddle.
Keywords: hyperbolic derivative, conformal (inner mapping) radius, bifurcations of critical points, Gakhov set, class of starlike functions, subordination conditions.
Received: 11.01.2013
Document Type: Article
UDC: 517.54
Language: Russian
Citation: A. V. Kazantsev, “On the exit out of the Gakhov set controlled by the subordination conditions”, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, 156, no. 1, Kazan University, Kazan, 2014, 31–43
Citation in format AMSBIB
\Bibitem{Kaz14}
\by A.~V.~Kazantsev
\paper On the exit out of the Gakhov set controlled by the subordination conditions
\serial Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki
\yr 2014
\vol 156
\issue 1
\pages 31--43
\publ Kazan University
\publaddr Kazan
\mathnet{http://mi.mathnet.ru/uzku1227}
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  • This publication is cited in the following 10 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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