MATHEMATICS

On an extremal problem for nonoverlapping domains

E. A. Pchelintsev^a, V. A. Pchelintsev<sup>b

a</sup> Tomsk State University, Tomsk, Russian Federation
^b Tomsk Polytechnic University, Tomsk, Russian Federation

Abstract: The paper considers the problem of finding the range of the functional $I=J(f(z_0), \overline{f(z_0)}, F(\zeta_0), \overline{F(\zeta_0)})$ defined on the class $\mathfrak{M}$ of functions pairs $(f(z), F(\zeta))$ that are univalent in the system of the disk and the interior of the disk, using the method of internal variations. We establish that the range of this functional is bounded by the curve whose equation is written in terms of elliptic integrals, depending on the parameters of the functional $I$.

Keywords: Method of internal variations, Univalent function, Nonoverlapping domains, Functional range, Elliptic integrals.

UDC: 517.54

MSC: 30C70

Received: 07.01.2018

Language: English

DOI: 10.17223/19988621/52/2

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