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

Voir la notice de l'article provenant de la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

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},
     language = {en},
     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/