Univalence and quasiconformal extension of an integral operator

TL;DR

This paper establishes new conditions for the analyticity, univalence, and quasiconformal extension of functions defined by an integral operator, enhancing existing criteria and revealing new relationships in complex analysis.

Contribution

It introduces novel univalence and quasiconformal extension criteria for integral operator-defined functions, refining previous results with Becker's method and connecting to known conditions.

Findings

Derived sufficient conditions for univalence and analyticity.

Provided quasiconformal extension criteria using Becker's method.

Unified and extended existing univalence conditions.

Abstract

In this paper we give some sufficient conditions of analyticity and univalence for functions defined by an integral operator. Next, we refine the result to a quasiconformal extension criterion with the help of the Becker's method. Further, new univalence criteria and the significant relationships with other results are given. A number of known univalence conditions would follow upon specializing the parameters involved in our main results.