Sharp univalence and sharp univalent covering domains for the class of holomorphic self-maps of a disc with two fixed boundary points

The class of holomorphic self-maps of the unit disc with two fixed boundary points, one of which is attracting, is under consideration. Maximal univalence and univalent covering domains are found for the functions in this class that satisfy a bound on the value of the angular derivative at the repelling boundary point.
Bibliography: 17 titles.