Avkhadiev–Lehto Type Constants in the Study of the Gakhov Class

Abstract

Avkhadiev's classes consist of holomorphicfunctions with a two-sided restriction on the module of thederivative. We study these classes in domains different from theunit disk. For the images of the domains under the mappings ofAvkhadiev's classes, we find conditions providing the uniquenessof critical point of the conformal radius. We use an analogue of the concept that Lehto applied to study univalence of functionssatisfying the conditions of Nehari type in domains conformallyequivalent to a disk.