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Univalence of mappings from half-plane to a polygonal domains with infinite sets of vertices

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Abstract

We apply solutions of the Hilbert boundary value problem with discontinuous coefficients and two-side curling at the infinity of logarithmic order to the construction of the formula of conformal mapping for a half-plane onto a polygonal domain with a countable set of vertices. We prove a sufficient condition of univalence of such mappings.

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Authors and Affiliations

  1. Kazan State University of Architecture and Engineering, Zelenaya ul. 1, Kazan, Tatarstan, 420043, Russia

    E. N. Karabasheva & P. L. Shabalin

Authors
  1. E. N. Karabasheva
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  2. P. L. Shabalin
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Correspondence to E. N. Karabasheva.

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Submitted by F. G. Avhadiev

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Karabasheva, E.N., Shabalin, P.L. Univalence of mappings from half-plane to a polygonal domains with infinite sets of vertices. Lobachevskii J Math 36, 144–153 (2015). https://doi.org/10.1134/S1995080215020080

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  • DOI: https://doi.org/10.1134/S1995080215020080

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