Note on the zeros of functions with univalent derivatives

Abstract

Let E denote the class of functions f(z) analytic in the unit disc D, normalized so that f(0)=0=f′(0)−1, such that each f(k)(z), k≥0 is univalent in D. In this paper we establish conditions for some functions to belong to class E.

Keywords

• univalent functions
• close-to-convex functions
• entire functions.