Even coefficient estimates for bounded univalent functions

Volume 58 / 1993

D. Prokhorov Annales Polonici Mathematici 58 (1993), 267-273 DOI: 10.4064/ap-58-3-267-273


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.


  • D. Prokhorov

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