Semi-convex hulls of analytic functions in the unit disk
For an analytic function / in the unit disk D we define the semi-convex hull Qf := j f{ze'')dt : 0 < e < TT, 2 G d | , which satisfies /(D) C Q/ C co/(D), and where co stands for the convex hull of a set. We characterize those / for which Q/ / C, and study the question whether the condition 0 ^ Qf implies that / is Univalent in D. Our investigation was triggered by the mean-value theorem ^ { f ^ / f dt : h<t2<tr + 2nY f e H\ earlier obtained by Danikas & Nestoridis [4]. 1991 Mathematics Subject Classification. Primary 30C55; Secondary 30C25