Quasinormal Families Of Meromorphic Functions

Let {fn} be a family of functions meromorphic on the unit disk?,whose zeros all have multiplicity at least 3;and let h(z)((?)0)be a function holomorphic on ?,E = {z|z ??,h(z)= 0}.In this paper,we prove that if f'n(z)?h(z)and no subsequence of {fn} is normal at some z0 ? ?,then z0 ? E and f'n(z)(?)h(z)on ?\E.In addition,we have fn(z)(?)h(?)d? for z??\E.n example is also provided to show that the quasinormal order of {fn} can be ositive infinity.