Rigidity at the boundary for holomorphic self-maps of the unit disk

We prove a rigidity theorem which generalizes a result due to Burns and Krantz (see[3]) for holomorphic self-maps in the unit disk of the complex plane. Essentially, we found that some conditions on the (boundary) Schwarzian derivative 0f a holomorphic self-map at specific points of the boundary of the disk may be sufficient to conclude that a map is a completely determined rational map.