On the Gakhov Equation in the Janowski Classes with Additional Parameter

Abstract

The Janowski class is characterized by a suitable disk in the right half-plane containing values of the functional ζf0 /f for all functions of this class. The set of such classes-disks forms a two-dimensional family ”filling” ∆ triangle. In our previous works, the maximum domain ∆0 ⊂ ∆ 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 ∆ × [0, 1].

Keywords

• gakhov equation
• gakhov set
• janowski classes
• hyperbolic derivative
• conformal (inner mapping) radius