Normal families of meromorphic functions with multiple zeros and poles

Let k be a positive integer with k 2 and let F be a family of functions meromorphic on a domain D in C, all of whose poles have multiplicity at least 3, and of whose zeros all have multiplicity at least k + 1. Let a(z) be a function holomorphic on D, a(z) ≡ 0. Suppose that for each f ∈ F, f (k)(z) = a(z) for z ∈ D. Then F is a normal family on D.  2004 Elsevier Inc. All rights reserved