Normal families and shared values of meromorphic functions

Mingliang Fang, and Lawrence Zalcman. "Normal families and shared values of meromorphic functions." Annales Polonici Mathematici 80.1 (2003): 133-141. <http://eudml.org/doc/280651>.

@article{MingliangFang2003,
abstract = {Let ℱ be a family of meromorphic functions on a plane domain D, all of whose zeros are of multiplicity at least k ≥ 2. Let a, b, c, and d be complex numbers such that d ≠ b,0 and c ≠ a. If, for each f ∈ ℱ, $f(z) = a ⇔ f^\{(k)\}(z) = b$, and $f^\{(k)\}(z) = d ⇒ f(z)= c$, then ℱ is a normal family on D. The same result holds for k=1 so long as b≠(m+1)d, m=1,2,....},
author = {Mingliang Fang, Lawrence Zalcman},
journal = {Annales Polonici Mathematici},
keywords = {normal families; shared values},
language = {eng},
number = {1},
pages = {133-141},
title = {Normal families and shared values of meromorphic functions},
url = {http://eudml.org/doc/280651},
volume = {80},
year = {2003},
}

TY - JOUR
AU - Mingliang Fang
AU - Lawrence Zalcman
TI - Normal families and shared values of meromorphic functions
JO - Annales Polonici Mathematici
PY - 2003
VL - 80
IS - 1
SP - 133
EP - 141
AB - Let ℱ be a family of meromorphic functions on a plane domain D, all of whose zeros are of multiplicity at least k ≥ 2. Let a, b, c, and d be complex numbers such that d ≠ b,0 and c ≠ a. If, for each f ∈ ℱ, $f(z) = a ⇔ f^{(k)}(z) = b$, and $f^{(k)}(z) = d ⇒ f(z)= c$, then ℱ is a normal family on D. The same result holds for k=1 so long as b≠(m+1)d, m=1,2,....
LA - eng
KW - normal families; shared values
UR - http://eudml.org/doc/280651
ER -