×

zbMATH — the first resource for mathematics

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.)
PDF BibTeX XML Cite
Full Text: DOI