Two sufficient conditions for the univalence of analytic functions

In this article we obtain sufficient conditions for the univalence of n-symmetric analytic functions in the region ¦¦>–1 and in the disk ¦¦<–1. We examine the question of univalent variation of functions analytic in ¦¦<–1 and mapping ¦¦=1 onto a contour with two zero angles. We give an application of these results to the fundamental converse boundary-value problems.Translated from Matematicheskie Zametki, Vol. 19, No. 3, pp. 331–346, March, 1976.In conclusion the author would like to thank L. A. Aksent'ev for his guidance, and those who took part in his seminar for their useful advice.