On a conjecture about univalent polynomials

Abstract

In this paper we prove a recent conjecture formulated by Dmitrishin, Smorodin and Stokolos about that certain polynomials are univalent in the unit disk. As a consequence we get an upper estimate for the Koebe radius of univalent polynomials.

These results was obtained by Brandt M., Variationsmethoden für in der Einheitskreisscheibe schlichte Polynome, Dissertation, Humboldt-Univ. Berlin, 1987