Exceptional functions and normal families of meromorphic functions with multiple zeros

Let k be a positive integer with k 2; let h( ≡ 0) be a holomorphic function which has no simple zeros in D; and let F be a family of meromorphic functions defined in D, all of whose poles are multiple, and all of whose zeros have multiplicity at least k +1. If, for each function f ∈ F, f (k)(z) = h(z), then F is normal in D. © 2007 Elsevier Inc. All rights reserved.