Two sufficient conditions for the univalence of analytic functions

Abstract

In this article we obtain sufficient conditions for the univalence of n-symmetric analytic functions in the region |ζ|>-1 and in the disk |ζ|<-1. We examine the question of univalent variation of functions analytic in |ζ|<-1 and mapping |ζ|=1 onto a contour with two zero angles. We give an application of these results to the fundamental converse boundary-value problems. © 1976 Plenum Publishing Corporation.