On a conjecture about univalent polynomials
Complex Variables
2020-09-15 v3 Classical Analysis and ODEs
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.
Cite
@article{arxiv.2002.12304,
title = {On a conjecture about univalent polynomials},
author = {Ilgiz R. Kayumov and Diana M. Khammatova},
journal= {arXiv preprint arXiv:2002.12304},
year = {2020}
}
Comments
These results was obtained by Brandt M., Variationsmethoden f\"ur in der Einheitskreisscheibe schlichte Polynome, Dissertation, Humboldt-Univ. Berlin, 1987