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.

中文翻译：

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Gakhov类研究中的Avkhadiev–Lehto类型常数

Avkhadiev的类由全纯函数组成，在导数的模块上有两个限制。我们在不同于单位磁盘的域中研究这些类。对于在阿夫哈迪耶夫类的映射下的域图像，我们找到了提供共形半径的临界点唯一性的条件。我们使用Lehto用于研究在与磁盘保形等效的域中满足Nehari类型条件的函数的单调性的概念的类似物。