Original Article
Kyungpook Mathematical Journal 2009; 49(2): 235-243
Published online June 23, 2009
Copyright © Kyungpook Mathematical Journal.
Meromorphic Function Sharing Two Small Functions with Its Derivative
Kai Liu, Xiao-guang Qi
School of Mathematics, Shandong University, Jinan, 250100 Shandong, P. R. China
In this paper, we deal with the problem of uniqueness of meromorphic functions that share two small functions with their derivatives, and obtain the following result which improves a result of Yao and Li: Let $f(z)$ be a nonconstant meromorphic function, $k>5$ be an integer. If $f(z)$ and $g(z)=a_{1}(z)f(z)+a_{2}(z)f^{(k)}(z)$ share the value $0$ CM, and share $b(z)$ IM, $overline{N}_{E}(r,f=0=f^{(k)})=S(r)$, then $fequiv g$, where $a_{1}(z)$,, $a_{2}(z)$ and $b(z)$ are small functions of $f(z)$.
Keywords: meromorphic function, uniqueness, sharing values