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Normal Families and Shared Values
Authors:Pang  Xuecheng; Zalcman  Lawrence
Institution:Department of Mathematics and Computer Science, Bar-Ilan University 52900 Ramat-Gan, Israel
Department of Mathematics, East China Normal University Shanghai 200062, P.R. China
Abstract:For f a meromorphic function on the plane domain D and a isin C,let Ef(a) = {z isin D: f(z) = a}. Let F be a family of meromorphicfunctions on D, all of whose zeros are of multiplicity at leastk. If there exist b != 0 and h > 0 such that for every f isin F,Ef(0) = Ef(k)(b) and 0 < |f(k+1)(z)| ≤ h whenever z isin Ef(0), thenF is a normal family on D. The case Ef(0) = Ø is a celebratedresult of Gu 5]. 1991 Mathematics Subject Classification 30D45,30D35.
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