This paper studies the unicity of meromorphic(resp. entire) functions of the form $f^nf^{\prime }$ and obtains the following main result: Let $f$ and $g$ be two non-constant meromorphic (resp. entire) functions, and let $a\in \mathbb {C}\backslash \lbrace 0\rbrace $ be a non-zero finite value. Then, the condition that $E_{3)}(a,f^nf^{\prime })=E_{3)}(a,g^ng^{\prime })$ implies that either $f=dg$ for some $(n+1)$-th root of unity $d$, or $f=c_1e^{cz}$ and $g=c_2e^{-cz}$ for three non-zero constants $c$, $c_1$ and $c_2$ with $(c_1c_2)^{n+1}c^2=-a^2$ provided that $n\ge 11$ (resp. $n\ge 6$). It improves a result of C. C. Yang and X. H. Hua. Also, some other related problems are discussed.
@article{108055,
author = {Xiao-Tian Bai and Qi Han},
title = {On unicity of meromorphic functions due to a result of Yang - Hua},
journal = {Archivum Mathematicum},
volume = {043},
year = {2007},
pages = {93-103},
zbl = {1164.30021},
mrnumber = {2336962},
language = {en},
url = {http://dml.mathdoc.fr/item/108055}
}
Bai, Xiao-Tian; Han, Qi. On unicity of meromorphic functions due to a result of Yang - Hua. Archivum Mathematicum, Tome 043 (2007) pp. 93-103. http://gdmltest.u-ga.fr/item/108055/
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