On the range of one complex-valued functional

V. A. Pchelintsev; E. A. Pchelintsev

doi:10.1134/S0037446615050146

On the range of one complex-valued functional

V. A. Pchelintsev, E. A. Pchelintsev

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

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.

Original language	English
Pages (from-to)	922-928
Number of pages	7
Journal	Siberian Mathematical Journal
Volume	56
Issue number	5
DOIs	https://doi.org/10.1134/S0037446615050146
State	Published - 1 Sep 2015
Externally published	Yes

Keywords

boundary function
functional
range
univalent function
variational method

ASJC Scopus subject areas

General Mathematics

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10.1134/S0037446615050146

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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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AU - Pchelintsev, E. A.

PY - 2015/9/1

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N2 - 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.

AB - 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.

KW - boundary function

KW - functional

KW - range

KW - univalent function

KW - variational method

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DO - 10.1134/S0037446615050146

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SP - 922

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JO - Siberian Mathematical Journal

JF - Siberian Mathematical Journal

IS - 5

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On the range of one complex-valued functional

Abstract

Keywords

ASJC Scopus subject areas

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