On a conjecture about univalent polynomials
Ilgiz R. Kayumov, Diana M. Khammatova
TL;DR
This paper proves a recent conjecture that certain polynomials are univalent in the unit disk, providing an upper estimate for the Koebe radius of univalent polynomials, advancing understanding in geometric function theory.
Contribution
It confirms a conjecture about univalence of specific polynomials and derives an upper bound for the Koebe radius, contributing to the theory of univalent functions.
Findings
Proof of the conjecture on univalent polynomials
Upper estimate for the Koebe radius
Advancement in geometric function theory
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.
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Taxonomy
TopicsAnalytic and geometric function theory · Holomorphic and Operator Theory · Meromorphic and Entire Functions