On theorems of yang and schwick

Abstract

Let D be a plane domain a meromorphic function on D and k a fixed positive integer. Let F be a collection of functions meromorphic on D, none of which have poles in common with φ. According to a result of Schwick (cf. Yang [9]), if each f ∊ F satisfies for z ∊ D then .F is a normal family. We give a very simple proof of this result, based on applying a suitable refinement of Zalcman's Lemma.