# Ruscheweyh's univalence criterion and quasiconformal extensions

## TL;DR

This paper refines Ruscheweyh's univalence criterion to include quasiconformal extensions using Becker’s method, providing solutions to open problems in the theory of univalent functions.

## Contribution

It introduces a refined quasiconformal extension criterion based on Ruscheweyh's work, advancing the understanding of univalent functions and their extensions.

## Key findings

- Established a new quasiconformal extension criterion
- Solved an open problem posed by Ruscheweyh
- Enhanced the theoretical framework for univalent functions

## Abstract

Ruscheweyh extended the work of Becker and Ahlfors on sufficient conditions for a normalized analytic function on the unit disk to be univalent there. In this paper we refine the result to a quasiconformal extension criterion with the help of Becker's method. As an application, a positive answer is given to an open problem proposed by Ruscheweyh.