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The normality criteria of meromorphic functions concerning shared fixed-points. (English) Zbl 1419.30021

Summary: We study the normality criteria of meromorphic functions concerning shared fixed-points; we obtain the following: Let \(\mathcal{F}\) be a family of meromorphic functions defined in a domain \(D\) and \(k \geq 2\) a positive integer. For every \(f \in \mathcal{F}\), all zeros of \(f\) are of multiplicity at least \(k + 2\) and all poles of \(f\) are multiple. If \(f f^{(k)}\) and \(g g^{(k)}\) share \(z\) in \(D\) for each pair of functions \(f\) and \(g\), then \(\mathcal{F}\) is normal.

MSC:

30D45 Normal functions of one complex variable, normal families
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References:

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