Some sufficient conditions for the univalence of an integral operator

TL;DR

This paper establishes new sufficient conditions for the univalence of an integral operator using subordination chains, also refining criteria for quasiconformal extensions, and encompasses known univalence conditions as special cases.

Contribution

It introduces novel sufficient conditions for univalence of integral operators and refines quasiconformal extension criteria, expanding the theoretical framework.

Findings

Derived new univalence criteria using subordination chains

Unified existing univalence conditions as special cases

Enhanced quasiconformal extension criteria

Abstract

Making use of the method of subordination chains, we obtain some sufficient conditions for the univalence of an integral operator. In particular, as special cases, our results imply certain known univalence criteria. A refinement to a quasiconformal extension criterion of the main result, is also obtained.