Even coefficient estimates for bounded univalent functions
Volume 58 / 1993
Annales Polonici Mathematici 58 (1993), 267-273
DOI: 10.4064/ap-58-3-267-273
Abstract
Extremal coefficient properties of Pick functions are proved. Even coefficients of analytic univalent functions f with |f(z)| < M, |z| < 1, are bounded by the corresponding coefficients of the Pick functions for large M. This proves a conjecture of Jakubowski. Moreover, it is shown that the Pick functions are not extremal for a similar problem for odd coefficients.
