Holomorphic self-maps of the unit disc with two fixed diametrically opposite boundary points and an invariant diameter are investigated. Asymptotically sharp estimates for domains of univalence are obtained for functions in such classes, which depend on the product of the angular derivatives at the boundary fixed points.

Bibliography: 16 titles.

中文翻译：

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具有不变直径的圆盘的全纯自映射的单价域的渐近尖锐的两侧估计

研究了具有两个固定直径相对边界点和不变直径的单位圆盘的全纯自映射。对于此类类中的函数，获得了对单价域的渐近尖锐估计，这取决于边界固定点处的角导数的乘积。

参考书目：16 题。