This article is cited in 1 paper

On the range of one complex-valued functional

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

a</sup> 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.

UDC: 517.54

Received: 04.01.2015

DOI: 10.17377/smzh.2015.56.514

 English version: Siberian Mathematical Journal, 2015, 56:5, 922–928

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