Several Normal Criteria of Meromorphic Functions

In this paper we discuss the relation for normalities between functions and their k order derivative, and we obtain some normal criteria of the family of meromorphic functions . Let Fbe the family of the Meromorphic functions on the unit disc , f∈F,all of whose zeros on the multiplicity at least k, a 1≠a 2 ,f∈F.If there exist positive numbers h 1,h 2 such that for f∈F,| f(z)|h 1, whenever f (k)(z)=a 1 or f (k)(z)=a 2 , |f (k)(z)|h 2 whenever f(z) = 0,then F is normal on the unit disc.