Some generalizations on the univalence of an integral operator and quasiconformal extensions

TL;DR

This paper develops new criteria using Loewner chains and Beckers's method to determine when certain integral operators produce univalent functions and admit quasiconformal extensions.

Contribution

It introduces generalized sufficient conditions for univalence and quasiconformal extendibility of functions defined by integral operators, refining previous results.

Findings

Established new univalence criteria for integral operator-defined functions

Refined quasiconformal extension conditions using Beckers's method

Provided a broader framework for analyzing integral operators in complex analysis

Abstract

By using the method of Loewner chains, we establish some sufficient conditions for the analyticity and univalency of functions defined by an integral operator. Also, we refine the result to a quasiconformal extension criterion with the help of Beckers's method.