On the Normal Meromorphic Functions
Bulletin of the Malaysian Mathematical Society, Tome 30 (2007) no. 2
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Let F be a family of functions meromorphic in D such that all the zeros of f ∈ F are of multiplicity at least k (a positive integer), and let E be a set containing k+4 points of the extended complex plane. If, for each function f ∈ F , there exists a constant M and such that (1-|z| 2 ) k |f (k) (z)|/(1+|f(z)| k+1 ) ≤ M whenever z ∈ {f(z) ∈ E, z ∈ D} , then F is a uniformly normal family in D , that is, sup {(1-|z| 2 )f # (z) : z ∈ D, f ∈ F } ∞ .
Classification :
30D45, 30D35
@article{BMMS_2007_30_2_a4,
author = {Rongping Zhu and Yan Xu},
title = {On the {Normal} {Meromorphic} {Functions}},
journal = {Bulletin of the Malaysian Mathematical Society},
year = {2007},
volume = {30},
number = {2},
url = {http://geodesic.mathdoc.fr/item/BMMS_2007_30_2_a4/}
}
Rongping Zhu; Yan Xu. On the Normal Meromorphic Functions. Bulletin of the Malaysian Mathematical Society, Tome 30 (2007) no. 2. http://geodesic.mathdoc.fr/item/BMMS_2007_30_2_a4/