Work

On univalent polynomials with critical points on the unit circle

Year: 2018

Type: article

Abstract: Brannan showed that a normalized univalent polynomial of the form (P(z)=z+a2 z2+...+ an-1zn-1+znn) is starlike if and only if (a2=...=an-1=0). We give a new and simple proof of his result, showing further that it is also equivalent to the membership of P in the Noshiro–Warschawski class of univalent functions whose derivative has positive real part in the disk. Both proofs are based on the Fejér lemma for trigonometric polynomials with positive real part.

Source: Complex Variables and Elliptic Equations

DOI: 10.1080/17476933.2017.1420065

Authors: María J. Martín, Dragan Vukotić

Institutions: University of Eastern Finland, Universidad Autónoma de Madrid

Language: English

Topic: Analytic and geometric function theory

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: Secretaría de Estado de Investigación, Desarrollo e Innovación

Awards: G468967724, G833396205