Abstract:
Holomorphic self-maps of the unit disc with boundary fixed points are investigated. In 1982, Cowen and Pommerenke established an interesting generalization of the classical Julia–Carathéodory theorem, which allowed them to derive an exact estimate for the derivative at the Denjoy–Wolff point on a class of functions with an arbitrary finite set of boundary fixed points. In this paper, we obtain a new generalization of the Julia–Carathéodory theorem, which contains Cowen–Pommerenke result as a special case, moreover, it is an effective tool for solving various problems on classes of functions with fixed points.
