Let be integrable over and positive in and the class of functions univalent in the unit disk and normalized as usual. The authors consider for ,
and resp. , where denotes the subclass of closed-to-convex functions.
They ask whether there are functions such that and show that for
decreasing on , . Furthermore they consider the class of functions holomorphic in normalized in the origin as usual for which lies in a halfplane bounded by a straight line through the origin and functions
They determine numbers such that the conclusion
holds and for some special they find for which , where is the class of starlike functions. For , , this solves a problem discussed before by many authors.