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On the Gakhov equation in the Janowski classes with additional parameter

A. V. Kazantsev

Institute of Computer Mathematics and Information Technologies, Kazan (Volga Region) Federal University, Kazan, Russia

Abstract: The Janowski class is characterized by a suitable disk in the right half-plane containing values of the functional $\zeta f'/f$ for all functions of this class. The set of such classes-disks forms a two-dimensional family “filling” $\Delta$ triangle. In our previous works, the maximum domain $\Delta'\subset\Delta$ of the parameters ensuring the uniqueness property of the (zero) root of the Gakhov equation for each function of the corresponding class was determined. In the present paper, such a domain is found for the families of the Janowski classes over $\Delta\times[0,1]$.

Keywords: Gakhov equation, Gakhov set, Janowski classes, hyperbolic derivative, conformal (inner mapping) radius.

UDC: 517.546.1

Received: 18.04.2014

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