The fifth coefficient for bounded univalent functions with real coefficients (Q2509967)

The author considers the class of bounded analytic univalent functions \(f\) of the unit disk with real coefficients satisfying the normalization conditions \(f(0)=0\), \(f^\prime(0)=c_1>0\). For any fixed \(c_1\) the author uses a modified method of \textit{M. Schiffer} [Proc. Lond. Math. Soc. (2) 44, 432--449 (1938; Zbl 0019.22201)] to find extremal values of the fifth coefficient and to determine functions for which these extremal values are attained.