A note on normal families of meromorphic functions concerning shared values (Q764550)

Summary: We study the normality of families of meromorphic functions related to a Hayman conjecture. We consider whether a family of meromorphic functions \(\mathcal F\) is normal in \(D\) if, for every pair of functions \(f\) and \(g\) in \(\mathcal F\), \(f' - af^n\) and \(g' - ag^n\) share the value \(b\) for \(n = 1, 2\) and \(3\), where \(a\) and \(b \neq 0\) are two finite complex numbers. Some examples show that the conditions in our results are the best possible.