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JMB Journal of Microbiolog and Biotechnology

OPEN ACCESS eISSN 0454-8124
pISSN 1225-6951
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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

Abstract

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