Abstract
Let a and b be two given meromorphic functions on a domain D. We study normality of the family \(\mathcal {F}\) of meromorphic functions that satisfy \(f(z)f ^{(k)}(z) = a(z) \Leftrightarrow f^{(k)}(z) = b(z)\) for every \(f\in \mathcal {F}\) on D. Examples are also given to show the necessity of the conditions in our results.
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