Geodesic
Normal families of meromorphic functions concerning shared functions
Kragujevac Journal of Mathematics, Tome 39 (2015) no. 2, p. 149

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It is mainly proved: Let $\mathfrak{F}$ be a family of meromorphic function in $\mathcal{D}$, $a(z)(\neq0)$ and $b(z)(\not\equiv0)$ be two holomorphic functions on $\mathcal{D}$. Suppose that admits the zeros of multiplicity at least 3 for each function $f \in \mathfrak{F}$. For each $f\in \mathfrak{F}$, if $f=a(z)\Leftrightarrow f'=b(z)$ , then $\mathfrak{F}$ is normal in $\mathcal{D}$. Some example shows that the multiplicity of zeros of $f$ is best in some sense. And the result of paper improve and supplement the result of Lei, Yang and Fang [J. Math. Anal. App. 364 (2010), 143-150].
Classification : 30D45
Keywords: Meromorphic functions, holomorphic functions, normal family, shared functions 
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     author = {Cheng-Xiong Sun},
     title = {Normal families of meromorphic functions concerning shared functions},
     journal = {Kragujevac Journal of Mathematics},
     pages = {149 },
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     number = {2},
     year = {2015},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KJM_2015_39_2_a3/}
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Cheng-Xiong Sun. Normal families of meromorphic functions concerning shared functions. Kragujevac Journal of Mathematics, Tome 39 (2015) no. 2, p. 149 . http://geodesic.mathdoc.fr/item/KJM_2015_39_2_a3/