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Sibirsk. Mat. Zh., 2015, Volume 56, Number 5, Pages 1154–1162 (Mi smj2704)  

This article is cited in 1 scientific paper (total in 1 paper)

On the range of one complex-valued functional

V. A. Pchelintseva, E. A. Pchelintsevb

a Institute of Physics and Technology, Tomsk Polytechnical University, Tomsk, Russia
b Tomsk State University, Faculty of Mechanics and Mathematics, Tomsk, Russia

Abstract: We solve the problem of finding the range $\Omega$ of one functional on the class of pairs of normalized univalent functions. Using the method of internal variations, we obtain a system of functional-differential 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.

Keywords: functional, range, variational method, boundary function, univalent function.

DOI: https://doi.org/10.17377/smzh.2015.56.514

Full text: PDF file (295 kB)
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English version:
Siberian Mathematical Journal, 2015, 56:5, 922–928

Bibliographic databases:

UDC: 517.54
Received: 04.01.2015

Citation: V. A. Pchelintsev, E. A. Pchelintsev, “On the range of one complex-valued functional”, Sibirsk. Mat. Zh., 56:5 (2015), 1154–1162; Siberian Math. J., 56:5 (2015), 922–928

Citation in format AMSBIB
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\paper On the range of one complex-valued functional
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\vol 56
\issue 5
\pages 1154--1162
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\transl
\jour Siberian Math. J.
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\vol 56
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\pages 922--928
\crossref{https://doi.org/10.1134/S0037446615050146}
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. E. A. Pchelintsev, V. A. Pchelintsev, “On an extremal problem for nonoverlapping domains”, Vestn. Tomsk. gos. un-ta. Matem. i mekh., 2018, no. 52, 13–24  mathnet  crossref  elib
  • Сибирский математический журнал Siberian Mathematical Journal
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