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.
@article{bwmeta1.element.bwnjournal-article-apmv58z3p267bwm,
author = {D. V. Prokhorov},
title = {Even coefficient estimates for bounded univalent functions},
journal = {Annales Polonici Mathematici},
volume = {58},
year = {1993},
pages = {267-273},
zbl = {0784.30010},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-apmv58z3p267bwm}
}
D. V. Prokhorov. Even coefficient estimates for bounded univalent functions. Annales Polonici Mathematici, Tome 58 (1993) pp. 267-273. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-apmv58z3p267bwm/
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