Regularity and growth conditions for fast escaping points of entire functions

Vasiliki Evdoridou

paper

Regularity and growth conditions for fast escaping points of entire functions

arXiv:1603.01519

Abstract

Let $f$ be a transcendental entire function. The quite fast escaping set, $Q (f)$ , and the set $Q_{2} (f),$ which was defined recently, are equal to the fast escaping set, $A (f),$ under certain conditions. In this paper we generalise these sets by introducing a family of sets $Q_{m} (f)$ , $m \in N .$ We also give one regularity and one growth condition which imply that $Q_{m} (f)$ is equal to $A (f)$ and we show that all functions of finite order and positive lower order satisfy $Q_{m} (f) = A (f)$ for any $m$ . Finally, we relate the new regularity condition to a sufficient condition for $Q_{2} (f) = A (f)$ introduced in recent work.