Abstract
Let \(F\) be a quasinormal family of meromorphic functions on D, all of whose zeros are multiple, and let ϕ be a holomorphic function univalent on D. Suppose that for any f ∊ \(F\) , f′(z) ≠ ϕ′(z) for z ∊ D. Then \(F\) is quasinormal of order 1 on D. Moreover, if there exists a compact set K ⊂ D such that each f ∊ \(F\). vanishes at two distinct points of K, then \(F\) is normal on D.
The authors were supported by the German-Israeli Foundation for Scientific Research and Development, G.I.F. Grant No. G-643-117.6/1999. The first author was also supported by the NNSF of China Approved No. 10271122.
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© 2005 Birkhäuser Verlag Basel/Switzerland
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Pang, X., Nevo, S., Zalcman, L. (2005). Quasinormal Families of Meromorphic Functions II. In: Eiderman, V.Y., Samokhin, M.V. (eds) Selected Topics in Complex Analysis. Operator Theory: Advances and Applications, vol 158. Birkhäuser Basel. https://doi.org/10.1007/3-7643-7340-7_13
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