Original Article
Kyungpook Mathematical Journal 2012; 52(1): 39-47
Published online March 23, 2012
Copyright © Kyungpook Mathematical Journal.
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
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