Abstract
LetF be a family of functions meromorphic in the plane domainD, all of whose zeros and poles are multiple. Leth be a continuous function onD. Suppose that, for eachf ≠F,f 1(z) εh(z) forz εD. We show that ifh(z) ≠ 0 for allz εD, or ifh is holomorphic onD but not identically zero there and all zeros of functions inF have multiplicity at least 3, thenF is a normal family onD.
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References
D. Bargmann, M. Bonk, A. Hinkkanen and G. J. Martin,Families of meromorphic functions avoiding continuous functions, Journal d’Analyse Mathématique79 (1999), 379–387.
W. Bergweiler and X. C. Pang,On the derivative of meromorphic functions with multiple zeros, Journal of Mathematical Analysis and Applications, to appear.
K. Deimling,Nonlinear Functional Analysis, Springer-Verlag, Berlin, 1985.
M. L. Fang,A note on a problem of Hayman, Analysis20 (2000), 45–49.
X. C. Pang and L. Zalcman,Normal families and shared values, The Bulletin of the London Mathematical Society32 (2000), 325–331.
Y. F. Wang and M. L. Fang,Picard values and normal families of meromorphic functions with multiple zeros, Acta Mathematica Sinica. New Series14 (1998), 17–26.
L. Zalcman,Normal families: new perspectives, Bulletin of the American Mathematical Society35 (1998), 215–230.
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Partially supported by the Shanghai Priority Academic Discipline and by the NNSF of China Approved No. 10271122.
Research supported by the German-Israeli Foundation for Scientific Research and Development, G.I.F. Grant No. G-643-117.6/1999.
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Pang, X., Zalcman, L. Normal families of meromorphic functions with multiple zeros and poles. Isr. J. Math. 136, 1–9 (2003). https://doi.org/10.1007/BF02807190
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DOI: https://doi.org/10.1007/BF02807190