On General Integral Operator of Analytic Functions

Abstract EN

Let Eβ be the integral operator defined by Eβz =β∫0ztβ-1f1′tα1f1t/tγ1P1ζ1t⋯fn′tαnfnt/tγnPnζntdt1/β, where each of the functions fi and Pi is, respectively, analytic functions and functions with positive real part defined in the open unit disk for all i=1,…,n.

The object of this paper is to obtain several univalence conditions for this integral operator.

Our main results contain some interesting corollaries as special cases.