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Lobachevskii Journal of Mathematics

, Volume 39, Issue 9, pp 1370–1376 | Cite as

Uniqueness of the Critical Point of the Conformal Radius: “Method of Déjà vu”

  • A. V. KazantsevEmail author
  • M. I. Kinder
Part 2. Special issue “Actual Problems of Algebra and Analysis” Editors: A. M. Elizarov and E. K. Lipachev
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Abstract

New conditions are constructed for the critical point of the conformal radius (hyperbolic derivative) to be unique where the mapping function is holomorphic and locally univalent in the unit disk. We use an approach based on the uniqueness research of the univalence conditions depending on the additional parameters. Such a research has been carried out for the univalence criteria due to Singhs, Szapiel and some other mathematicians.

Keywords and phrases

Conformal radius inner radius of domain hyperbolic derivative critical points of conformal radius Gakhov equation 

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Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  1. 1.Kazan (Volga Region) Federal UniversityKazanRussia

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