Julia directions of meromorphic functions and their derivatives

Abstract

We prove that if a transcendental meromorphic function has no Julia direction and is bounded on a path to $ \infty $ then there is a common Julia direction for all derivatives. Related statements are obtained under the assumption that f is $ o(\sqrt{\mid z \mid}) $ or $ O(\sqrt{\mid z \mid}) $ on a path to $ \infty $ . Further we disprove a conjecture of Frank and Wang by means of a counterexample.