Normal functions and \(\alpha\)-normal functions (Q1586082)

This paper concerns some inequalities concerning a normal meromorphic function in the unit disc due to \textit{P. Lappan} [Ann. Acad. Sci. Fenn., Ser. A I 3, 301-310 (1977; Zbl 0387.30018)]. In particular the author proves that if a meromorphic function \(f\) satisfies one of these inequalities, then \(f\) is a normal function. He also extends the result to the \(\alpha\)-normal functions.