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On the range of one complex-valued functional

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Abstract

We solve the problem of finding the range Ω of one functional on the class of pairs of normalized univalent functions. Using the method of internal variations, we obtain a system of functionaldifferential equations for the boundary functions solved in quadratures. We prove that the range of the functional is some disk centered at the origin of a radius depending on the parameters of the functional.

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Authors and Affiliations

  1. Tomsk Polytechnic University, Tomsk, Russia

    V. A. Pchelintsev

  2. Tomsk State University, Tomsk, Russia

    E. A. Pchelintsev

Authors
  1. V. A. Pchelintsev
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  2. E. A. Pchelintsev
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Correspondence to V. A. Pchelintsev.

Additional information

Original Russian Text Copyright © 2015 Pchelintsev V.A. and Pchelintsev E.A.

Tomsk. Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 56, No. 5, pp. 1154–1162, September–October, 2015; DOI: 10.17377/smzh.2015.56.514.

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Pchelintsev, V.A., Pchelintsev, E.A. On the range of one complex-valued functional. Sib Math J 56, 922–928 (2015). https://doi.org/10.1134/S0037446615050146

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  • DOI: https://doi.org/10.1134/S0037446615050146

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