On meromorphic univalent functions omitting a disc (Q1086380)

Let \(\Sigma_ b\), \(b\in (0,1)\), denote the class of functions \[ H(z)=z+\sum^{\infty}_{n=0}A_ nz^{-n},\quad 1<| z|, \] holomorphic, univalent and such that \(| H(z)| >b\). In this paper, Launonen's inequality [\textit{E. Launonen}, Ann. Acad. Sci. Fenn., Ser. A I, Diss. 1, 1-34 (1975; Zbl 0323.30017)] is applied to find sharp inequalities for the coefficients of functions inverse to odd \(\Sigma_ b\)-functions. The result extends the corresponding estimation due to \textit{E. Netanyahu} [Can. J. Math. 17, 335-341 (1965; Zbl 0148.308)] and \textit{G. Schober} [Proc. Am. Math. Soc. 67, 111-116 (1977; Zbl 0374.30013)], from \(b=0\) to the whole interval (0,1).