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 alpha(\\.\\), and f ixed-point-free, then there exists xi is an element of delta B such that th e sequence {f(n)} of the iterates of f converges in the compact-open topolo gy to the constant map taking the value xi. (C) 1999 Academic Press.