Normal families of meromorphic functions concerning shared functions
Kragujevac Journal of Mathematics, Tome 39 (2015) no. 2, p. 149
Voir la notice de l'article provenant de la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts
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
Keywords: Meromorphic functions, holomorphic functions, normal family, shared functions
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/
@article{KJM_2015_39_2_a3,
author = {Cheng-Xiong Sun},
title = {Normal families of meromorphic functions concerning shared functions},
journal = {Kragujevac Journal of Mathematics},
pages = {149 },
year = {2015},
volume = {39},
number = {2},
language = {en},
url = {http://geodesic.mathdoc.fr/item/KJM_2015_39_2_a3/}
}