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| Volume 30 • Number 2 • 2007 |
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On the Normal Meromorphic Functions
Rongping Zhu and Yan Xu
Abstract.
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} < ∞ .
2000 Mathematics Subject Classification: 30D45, 30D35
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