## On the Fekete-Szegő problem and argument inequality for strongly quasi-convex functions.(English)Zbl 0979.30008

Let $${\mathcal Q}(\beta)$$ be the class of normalized strongly quasiconvex functions of order $$\beta$$ in the open unit disc. Sharp Fekete-Szegö inequalities are obtained for functions belonging to the class $${\mathcal Q}(\beta)$$. The author also considers the integral preserving properties in a sector. For the principal proofs the author used the very known “admisible functions method” (differential subordination method) introduced by P. T Mocanu and S. S Miller.

### MSC:

 30C45 Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.)