Univalence of a certain quartic function

TL;DR

This paper provides a concise proof demonstrating that a specific quartic polynomial is univalent, contributing to the understanding of univalent functions in complex analysis.

Contribution

It offers a new, simplified proof of the univalence of a particular quartic polynomial, expanding the class of known univalent functions.

Findings

The polynomial is univalent in the complex plane.

The proof is shorter and more straightforward than previous methods.

Supports further research into polynomial univalence.

Abstract

We give a short proof that the quartic polynomial $f(z)=\frac 1 6 z^{4} + \frac 2 3 z^{3} + \frac 7 6 z^{2} + z$ is univalent.