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Fekete-Szegö problem for a class defined by an integral operator. (English) Zbl 1196.30013
Summary: By making use of an integral operator due to Noor, a new subclass of analytic functions, denoted by $$k-\mathcal{UCV}_n$$ ($$n \in N_{0} := \{0,1,2,\cdots \}$$; $$0 \leq k < \infty$$), is introduced. For this class, the Fekete-Szegö problem is completely settled. The results obtained here also give the Fekete-Szegö inequalities for the classes of $$k$$-uniformly convex functions and $$k$$-parabolic starlike functions.

##### MSC:
 30C45 Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.)
##### Keywords:
Fekete-Szegö problem; convex function; starlike function
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