A Schwarz lemma at the boundary using the Julia-Wolff-Carathéodory type condition on finite dimensional irreducible bounded symmetric domains

In this paper, we prove a Schwarz lemma at the boundary for holomorphic self-mappings f of finite dimensional irreducible bounded symmetric domains without assuming the boundary regularity of f. Our result generalizes the previous results obtained for holomorphic self-mappings f of the Euclidean unit ball, or of the classical Cartan domains of type I and of type II which are smooth up to the boundary.