An Extension of a Normality Result of D. Drasin and H. Chen & X. Hua for Analytic Functions

Abstract

We show that if an entire function f satisfies $$af^n(z) + f^{(k)}(z) + P\lbrack f \rbrack(z) \ne 0$$ for all z ∈ C, for some n ≥ 2, k ≥ 1, a ≠ 0, and with P a differential polynomial of a certain form, then f must be a constant. We also prove the corresponding normality criterion where the coefficients are meromorphic functions. This generalizes results of Hayman [7], Drasin [5] and Chen and Hua [2].