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

Abstract:

      In this paper, we obtain the following normal criterion: Let ${\cal F}$ be a family of meromorphic functions in domain $D\subset {\bf C}$, 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 $f(z)\in{\cal F}$, $f(z)$ shares $a(z)$ IM with $L(f)$ on $D$, then ${\cal F}$ 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.