On Lappan's five-point theorem
\textit{A. Hinkkanen} [N. Z. J. Math. 22, No. 2, 39--41 (1993; Zbl 0796.30029)] and \textit{P. Lappan} [Rev. Roum. Math. Pures Appl. 39, No. 7, 691--702 (1994; Zbl 0843.30031)] proved that a family \(\mathfrak{F}\) of meromorphic functions in a domain \(D \subset \mathbb{C}\) is normal if and only if for each compact set \(K \subset D\), there exist a set \(E = E(K) \subset \widehat{\mathbb{C}}\) containing at least five distinct points and a positive constant \(M = M(K)\) such that \(\displaystyle \max_{z \in K \cap f^{-1}(E)} f^{\#}(z) \leq M\) for all \(f \in \mathfrak{F}\). In the paper under review the authors prove an analogue of the `if' part of the above result for a set \(E = E(K)\) containing four and three distinct points. In addition to the spherical derivative of the members of \(\mathfrak{F}\) their results involve also the sperical derivative of the first and the second derivatives. They further prove similar results for \(\phi\)-normal functions.
scientific article; zbMATH DE number 6707035