On conditions for univalence of some integral operators

Abstract

In this paper, we obtain new univalence conditions for the integral operators F [|δ|] (z) and G [|δ|] (z) of analytic functions defined in the open unit disk.max |z|≤1 1 − |z| 2 · |z| · |z|+|a 2 | 1+|a 2 ||z| , then Fγ(z) = z 0 f (t) t γ dt *

Kudriasov Type Univalence Criteria for Some Integral Operators

“…For example, the result obtained by Pascu in [3] is also known as an improvement of Becker's univalence criteria. This result or other similar generalizations of Becker's univalence criteria have been used further to derive new univalence criteria for integral operators (see, e.g., some relatively recent works as [1,5,6]). In this paper we use Pascu improvement of Becker's univalence criteria and also another univalence condition for a function to be univalent, given by Kudriasov in [2].…”

Classes of meromorphic multivalent functions with Montel’s normalization

“…Several authors (e.g., see [4,5,6,8,10,11,15,16]), obtained many sufficient conditions for the univalency of the integral operators…”

On Univalence of Integral Operators

“…Recently the problem of univalence of some generalized integral operators have discussed by many authors such as: (see [2]- [8], [10], [14]- [16] …”