| Normality Family and Shared Functions by Meromorphic Functions and Its Differential Polynomials |
| Received:May 16, 2006 Revised:March 23, 2007 |
| Key Words:
meromorphic functions differential polynomials normal criterion shared functions.
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| Fund Project:the ``11.5'' Research \& Study Programe of SWUST (No.\,06zx2116). |
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| 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. |
| Citation: |
| DOI:10.3770/j.issn:1000-341X.2008.03.012 |
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