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by
Shahar Nevo

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...tiplicity at least k. Then F is normal in D if and only if { |f (k)| 1 + |f |k+1 : f ∈ F } is locally uniformly bounded in D. The direction “=⇒” holds without the assumption on the multiplicities. In =-=[10]-=- a new proof of Theorem B was given which avoids the use of Nevanlinna theory. Finally, Y. Xu [11] proved the following extension of Hinkkanen’s normality result to higher derivatives. Theorem C. Let ...

by
Roi Bar, Shahar Nevo
, 2013

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...(z) ≥ C for all z ∈ D and all f ∈ F . Then F is normal in D. Hence, the condition |f ′| 1+|f |2 (z) = f#(z) ≥ C can be considered as a differential inequality that constitutes normality. In [8], [2], =-=[6]-=- and [5] we studied more general differential inequalities, involving higher derivatives, with respect to the question whether they constitute normality or at least quasi-normality. Before summarizing...

by
Qiaoyu Chen

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... domain D, such that each f ∈ F has zeros only of multiplicities≥ k , k ∈ N . Then F is normal in D if and only if the family{ |f (k)(z)| 1 + |f(z)|k+1 : f ∈ F } is locally uniformly bounded in D. In =-=[6]-=-, the second and the third authors gave a counterexample to the validity of Theorem LX, without the condition on the multiplicities of zeros for the case k = 2. Concerning differential inequalities wi...

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