On the Gakhov equation in the Janowski classes with additional parameter
Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 157 (2015) no. 1, pp. 35-43
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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.
@article{UZKU_2015_157_1_a3,
author = {A. V. Kazantsev},
title = {On the {Gakhov} equation in the {Janowski} classes with additional parameter},
journal = {U\v{c}\"enye zapiski Kazanskogo universiteta. Seri\^a Fiziko-matemati\v{c}eskie nauki},
pages = {35--43},
publisher = {mathdoc},
volume = {157},
number = {1},
year = {2015},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/UZKU_2015_157_1_a3/}
}
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A. V. Kazantsev. On the Gakhov equation in the Janowski classes with additional parameter. Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 157 (2015) no. 1, pp. 35-43. http://geodesic.mathdoc.fr/item/UZKU_2015_157_1_a3/