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eISSN 0454-8124
pISSN 1225-6951

### Original Article

Kyungpook Mathematical Journal 2012; 52(1): 39-47

Published online March 23, 2012

### Further Results about the Normal Family of Meromorphic Functions and Shared Sets

Jianming Qi1 , Guowei Zhang2, Linlin Zhou3

1Department of Mathematics and Physics, Shanghai Dianji University, Shanghai, 200240, China
2School of Mathematics and Statistics, Anyang Normal University, Anyang, 455002, China
3Department of Mathematics , Zhenjiang watercraft college 212003, China

Received: March 23, 2012; Revised: March 23, 2012; Accepted: March 23, 2012

### Abstract

Let $mathcal{F}$ be a family of meromorphic functions in a domain $D$, and let $k$, $n(geq 2)$ be two positive integers, and let $S={a_1, a_2,..., a_n}$, where $a_1, a_2,..., a_n$ are distinct finite complex numbers. If for each $finmathcal{F}$, all zeros of $f$ have multiplicity at least $k+1$, $f$ and $G(f)$ share the set $S$ in $D$, where $G(f)=P(f^{(k)})+H(f)$ is a differential polynomial of $f$, then $mathcal{F}$ is normal in $D$.

Keywords: Meromorphic functions, Nevanlinna theory, Normal family, Share value