Normality criteria for families of zero-free meromorphic functions

Jun-Fan Chen. "Normality criteria for families of zero-free meromorphic functions." Annales Polonici Mathematici 115.1 (2015): 89-98. <http://eudml.org/doc/280834>.

@article{Jun2015,
abstract = {Let ℱ be a family of zero-free meromorphic functions in a domain D, let n, k and m be positive integers with n ≥ m+1, and let a ≠ 0 and b be finite complex numbers. If for each f ∈ ℱ, $f^m + a(f^\{(k)\})ⁿ - b$ has at most nk zeros in D, ignoring multiplicities, then ℱ is normal in D. The examples show that the result is sharp.},
author = {Jun-Fan Chen},
journal = {Annales Polonici Mathematici},
keywords = {meromorphic function; normal family; zero-free},
language = {eng},
number = {1},
pages = {89-98},
title = {Normality criteria for families of zero-free meromorphic functions},
url = {http://eudml.org/doc/280834},
volume = {115},
year = {2015},
}

TY - JOUR
AU - Jun-Fan Chen
TI - Normality criteria for families of zero-free meromorphic functions
JO - Annales Polonici Mathematici
PY - 2015
VL - 115
IS - 1
SP - 89
EP - 98
AB - Let ℱ be a family of zero-free meromorphic functions in a domain D, let n, k and m be positive integers with n ≥ m+1, and let a ≠ 0 and b be finite complex numbers. If for each f ∈ ℱ, $f^m + a(f^{(k)})ⁿ - b$ has at most nk zeros in D, ignoring multiplicities, then ℱ is normal in D. The examples show that the result is sharp.
LA - eng
KW - meromorphic function; normal family; zero-free
UR - http://eudml.org/doc/280834
ER -