Two-sided estimates for domains of univalence for classes of holomorphic self-maps of a disc with two fixed points

We investigate the class of holomorphic maps of a disc into itself that have an interior and a boundary fixed point, as well as the class of holomorphic maps of a half-plane into itself that have a fixed point in the interior of the domain and a fixed point at infinity. Two-sided estimates for domains of univalence are obtained for these function classes in terms of the values of the angular derivative at the boundary fixed point and the position of the interior fixed point.
Bibliography: 21 titles.