Computational Methods and Function Theory 4 (2004), No. 2, 299--314
Copyright Heldermann Verlag 2004
Jianming Chang
jmwchang@pub.sz.jsinfo.net , Department of Mathematics, Nanjing Normal University, Nanjing 210097, and Department of Mathematics, Changshu Institute of Technology, Changshu, Jiangsu 215500, P. R. China.
Mingliang Fang
mlfang@pine.njnu.edu.cn , Department of Applied Mathematics, South China Agricultural University, Guangzhou 510642, P. R. China.
Degui Yang
dyang@scau.edu.cn , Department of Applied Mathematics, South China Agricultural University, Guangzhou 510642, P. R. China.
Let $f$ be a non-constant meromorphic function satisfying $ff'\neq0$, and let $a\not\equiv 0$ be a small function related to $f$. If $f(z)=a(z)$ whenever $f'(z)=a(z)$, then either $f\equiv f'$ or $f(z)=2a/(1-ce^{-2z})$, where $a, c$ are two non-zero constants and $a(z)\equiv a$.
Keywords: Meromorphic function, unicity, small function.
MSC 2000: 30D35.
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