On some conditions for schlichtness of analytic functions

Abstract The aim of this paper is to give some conditions for univalence of analytic functions in the unit disc | z | 1 . We consider starlike functions such that z f ′ ( z ) ∕ f ( z ) lies in a vertical strip. In the second part we present some conditions on z f ′ ′ ( z ) ∕ f ′ ( z ) for f to be univalent.