Univalence and quasiconformal extension of an integral operator

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.