Geodesic
Normal Families of Meromorphic Functions Sharing a Holomorphic Function
Kragujevac Journal of Mathematics, Tome 38 (2014) no. 2, p. 273 .

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Let $k$ be a positive integer, and $m$ be an even number. Suppose that $a(z)(\not\equiv 0)$ is a holomorphic function with zeros of multiplicity $m$ in a domain $D$. Let $\cal F$ be a family of meromorphic functions in a domain $D$ such that each $f\in\cal F$ have zeros of multiplicity at least $k+1+m$ and poles of multiplicity at least $m+1$. It is mainly proved that for each pair $(f,g)\in\cal F$, if $ff^{(k)}$ and $gg^{(k)}$ share $a(z)$ IM, then $\cal F$ is normal in $D$. This result improves Hu and Meng's results published in Journal of Mathematical Analysis and Applications (2009, 2011), and also Jiang and Gao's result in Acta Matematica Scientia (2012).
Classification : 30D35 30D45
Keywords: meromorphic functions, holomorphic functions, normal family, sharing holomorphic function 
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     author = {Cheng-Xiong Sun},
     title = {Normal {Families} of {Meromorphic} {Functions} {Sharing} a {Holomorphic} {Function}},
     journal = {Kragujevac Journal of Mathematics},
     pages = {273 },
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     number = {2},
     year = {2014},
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     url = {http://geodesic.mathdoc.fr/item/KJM_2014_38_2_a5/}
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Cheng-Xiong Sun. Normal Families of Meromorphic Functions Sharing a Holomorphic Function. Kragujevac Journal of Mathematics, Tome 38 (2014) no. 2, p. 273 . http://geodesic.mathdoc.fr/item/KJM_2014_38_2_a5/