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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.)
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