The normality criteria of meromorphic functions concerning shared fixed-points (Q2321473)

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.