Geodesic
Normality criteria for families of zero-free meromorphic functions
Jun-Fan Chen1
1 Department of Mathematics Fujian Normal University Fuzhou 350117, Fujian Province, P.R. China
Annales Polonici Mathematici, Tome 115 (2015) no. 1, pp. 89-98

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

Let $\mathcal F$ be a family of zero-free meromorphic functions in a domain $D$, let $n$, $k$ and $m$ be positive integers with $n\geq m+1$,\vadjust {\vskip 1pt} and let $a\not =0$ and $b$ be finite complex numbers. If for each $f\in \mathcal F$, $f^m+a(f^{(k)})^n-b$ has at most $nk$ zeros in $D$, ignoring multiplicities, then $\mathcal F$ is normal in $D$. The examples show that the result is sharp.
DOI : 10.4064/ap115-1-7
Keywords: mathcal family zero free meromorphic functions domain positive integers geq vadjust vskip finite complex numbers each mathcal f n b has zeros ignoring multiplicities mathcal normal examples result sharp

Jun-Fan Chen 1

1 Department of Mathematics Fujian Normal University Fuzhou 350117, Fujian Province, P.R. China 
@article{10_4064_ap115_1_7,
     author = {Jun-Fan Chen},
     title = {Normality criteria for families of
 zero-free meromorphic functions},
     journal = {Annales Polonici Mathematici},
     pages = {89--98},
     publisher = {mathdoc},
     volume = {115},
     number = {1},
     year = {2015},
     doi = {10.4064/ap115-1-7},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4064/ap115-1-7/}
}
TY  - JOUR
AU  - Jun-Fan Chen
TI  - Normality criteria for families of
 zero-free meromorphic functions
JO  - Annales Polonici Mathematici
PY  - 2015
SP  - 89
EP  - 98
VL  - 115
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.4064/ap115-1-7/
DO  - 10.4064/ap115-1-7
LA  - en
ID  - 10_4064_ap115_1_7
ER  - 
%0 Journal Article
%A Jun-Fan Chen
%T Normality criteria for families of
 zero-free meromorphic functions
%J Annales Polonici Mathematici
%D 2015
%P 89-98
%V 115
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.4064/ap115-1-7/
%R 10.4064/ap115-1-7
%G en
%F 10_4064_ap115_1_7
Jun-Fan Chen. Normality criteria for families of
 zero-free meromorphic functions. Annales Polonici Mathematici, Tome 115 (2015) no. 1, pp. 89-98. doi: 10.4064/ap115-1-7

Cité par Sources :