Normality of meromorphic functions whose derivatives have 1-points

摘要

Let k be a positive integer and let be a family of functions meromorphic in a plane domain D, all of whose zeros have multiplicity at least k + 3. If there exists a subset E of D which has no accumulation points in D such that for each function , f (k)(z) − 1 has no zeros in , then is normal. The number k + 3 is sharp. The proof uses complex dynamics.