Normal Families and Shared Values |
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Authors: | Pang, Xuecheng Zalcman, Lawrence |
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Affiliation: | 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 |
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Abstract: | For f a meromorphic function on the plane domain D and a C,let f(a) = {z 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 F,f(0) = f(k)(b) and 0 < |f(k+1)(z)| h whenever z f(0), thenF is a normal family on D. The case f(0) = Ø is a celebratedresult of Gu [5]. 1991 Mathematics Subject Classification 30D45,30D35. |
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