Libera, Richard J.; Złotkiewicz, Eligiusz J. Bounded Montel univalent functions. (English) Zbl 0674.30011 Colloq. Math. 56, No. 1, 169-177 (1988). Let a be fixed, \(0<a<1\), and let f be regular and univalent in \(\Delta =\{z:\) \(| z| <1\}\). The function f is in Montel’s class M(a) if \(f(0)=0\), \(f(a)=a\). The subclass of M(a) whose members F are bounded by M (\(| F(z)| \leq M\) for \(z\in \Delta)\) is denoted by M(a;M). In the paper, some properties of functions in M(a;M) are established. For example, if \(F(z)=A_ 1z+A_ 2z^ 2+...\), \(F\in M(a;M)\), the authors obtain sharp upper and lower bounds for \(| A_ 1|\). They also obtain two covering theorems. Reviewer: Z.Jakubowski Cited in 2 Documents MSC: 30C45 Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.) Keywords:bounded Montel univalent functions PDFBibTeX XMLCite \textit{R. J. Libera} and \textit{E. J. Złotkiewicz}, Colloq. Math. 56, No. 1, 169--177 (1988; Zbl 0674.30011) Full Text: DOI