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NORMAL FAMILIES AND SHARED VALUES

Published online by Cambridge University Press:  01 May 2000

XUECHENG PANG  and
LAWRENCE ZALCMAN
XUECHENG PANG
Affiliation:
Department of Mathematics and Computer Science, Bar-Ilan University, 52900 Ramat-Gan, Israel
LAWRENCE ZALCMAN
Affiliation:
Department of Mathematics, East China Normal University, Shanghai 200062, P.R. China
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Abstract

For f a meromorphic function on the plane domain D and a ∈ [Copf ], let Ēf(a) = {z ∈ D[ratio ]f(z) = a}. Let [Fscr ] be a family of meromorphic functions on D, all of whose zeros are of multiplicity at least k. If there exist b ≠ 0 and h > 0 such that for every f ∈ [Fscr ], Ēf(0) = Ēf(k)(b) and 0 < [mid ]f(k+1)(z)[mid ] [les ] h whenever z ∈ Ēf(0), then [Fscr ] is a normal family on D. The case Ēf(0) = Ø is a celebrated result of Gu [5].

Type
NOTES AND PAPERS
Information
Bulletin of the London Mathematical Society , Volume 32 , Issue 3 , May 2000 , pp. 325 - 331
Copyright
© The London Mathematical Society 2000

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