Normality and shared values concerning differential polynomials (Q973769)

Let \({\mathcal F}\) be a family of meromorphic functions in a domain \(D\), and let \(P\) be a polynomial with either \(\deg P \geq 3\) or \(\deg P=2\), and \(P\) having only one zero. In this paper, the authors prove that if there is a non-zero complex number \(b\) such that, for any \(f \in {\mathcal F}\) and \(g \in {\mathcal F}\), \(P(f)f'\) and \(P(g)g'\) share \(b\) in \(D\), then \({\mathcal F}\) is normal in \(D\). The authors also give two examples showing that the theorem fails when \(\deg P=1\) or \(b=0\).