Abstract
AbstractSuppose that f(z) is a transcendental entire function and that the Fatou set F(f)≠∅. Set
and
where the supremum supU is taken over all components of F(f). If B1(f)<∞ or B2(f)<∞, then we say F(f) is strongly uniformly bounded or uniformly bounded respectively. We show that, under some conditions, F(f) is (strongly) uniformly bounded.
Publisher
Cambridge University Press (CUP)