Normality Family and Shared Functions by Meromorphic Functions and Its Differential Polynomials

In this paper, we obtain the following normal criterion： Let F be a family of mero-morphic functions in domain D belong to C, all of whose zeros have multiplicity k ＋ 1 at least. If there exist holomorphic functions α（z） not vanishing on D, such that for every function f（z） ∈F, f（z） shares α（z） IM with L（f） on D, then F is normal on D, where L（f） is linear differential polynomials of f（z） with holomorphic coefficients, and k is some positive numbers. We also proved coressponding results on normal functions.

In this paper,we obtain the following normal criterion:Let F be a family of mero- morphic functions in domain DC,all of whose zeros have multiplicity k+1 at least.If there exist holomorphic functions a(z)not vanishing on D,such that for every function f(z)∈F, f(z)shares a(z)IM with L(f)on D,then F is normal on D,where L(f)is linear differential polynomials of f(z)with holomorphic coefficients,and k is some positive numbers.We also proved coressponding results on normal functions.