Exceptional functions and normal families of meromorphic functions with multiple zeros

Let k be a positive integer with k >= 2; let h(not equivalent to 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 is an element of F, f((k))(z) not equal h(z), then F is normal in D. (c) 2007 Elsevier Inc. All rights reserved.