Sufficient conditions for univalence of analytic functions

TL;DR

This paper develops a unified method to establish new sharp criteria for the univalence of analytic functions within the unit disc, expanding the understanding of when such functions are injective.

Contribution

It introduces a novel unified approach to derive sharp univalence criteria for analytic functions, covering various parameter-dependent families.

Findings

Developed a unified method for univalence criteria

Identified several new sharp univalence conditions

Extended criteria to parameter-dependent families

Abstract

The article discusses criteria for univalence of analytic functions in the unit disc. Various families of analytic functions depending on real parameters are considered. A unified method for creating new sets of conditions ensuring univalence is presented. Applying this method we are able to find several families of new sharp criteria for univalence.