On the univalence of an integral on subclasses of meromorphic functions

Abstract

We study the integral operator Pλ[f](ζ) = ∫ ζ0 ζ(f′(t))λ dt, |ζ| > 1, acting on the class ∑ of functions meromorphic and univalent in the exterior of the unit disk. We refine the ranges of the parameter λ for which the operator preserves univalence either on ∑ or on its subclasses consisting of convex functions. As a consequence, a two-sided estimate is deduced for the separating constant in the sufficient condition for the univalent solvability of exterior inverse boundary-value problems. ©2001 Plenum Publishing Corporation.