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Hankel determinant for starlike and convex functions. (English) Zbl 1137.30308

From the summary: Denote \({\mathcal S}\) to be the class of functions which are analytic, normalised and univalent in the open unit disc \({\mathcal D}= \{z:|z|<1\}\). We denote by \({\mathcal S}^*\) and \({\mathcal C}\) the classes of starlike and convex functions. This paper focuses on attaining sharp upper bounds for the functional \(|a_2a_4-a_3^2|\) for functions \(f(z)= z+\sum_{n=2}^\infty a_nz^n\) belonging to \({\mathcal S}^*\) and \({\mathcal C}\).

MSC:

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