The Denjoy–Wolff Theorem for Condensing Holomorphic Mappings

If B is the open unit ball of a strictly convex Banach space (X, ‖·‖) and f: B→B is holomorphic, condensing with respect to α‖·‖, and fixed-point-free, then there exists ξ∈∂B such that the sequence lcub;fn} of the iterates of f converges in the compact-open topology to the constant map taking the value ξ.