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A normality criterion involving rotations and dilations in the argument. (English) Zbl 1285.30019

The author proves that a family \(\mathfrak{F}\) of analytic functions in the unit disc \(D\) having zeros of multiplicity at least \(k\) satisfying the condition \(f^{n}(z)f^{(k)}(xz)\) \( \neq 1\) for all \(z \in D\) and \(f \in \mathfrak{F}\) (where \(n \geq 3\), \(k \geq 1\) and \(0 < \mid x \mid \leq 1\)) is normal at the origin. He uses modified Nevanlinna theory, as introduced by himself [Comput. Methods Funct. Theory 10, No. 1, 97–109 (2010; Zbl 1207.30047)], to prove the result. Some related Picard type theorems are also proved.

MSC:

30D45 Normal functions of one complex variable, normal families

Citations:

Zbl 1207.30047
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References:

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