Abstract
Avkhadiev's classes consist of holomorphic functions with a two-sided restriction on the module of the derivative. We study these classes in domains different from the unit disk. For the images of the domains under the mappings of Avkhadiev's classes, we find conditions providing the uniqueness of critical point of the conformal radius. We use an analogue of the concept that Lehto applied to study univalence of functions satisfying the conditions of Nehari type in domains conformally equivalent to a disk.
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