SHARP BOUNDS OF SOME COEFFICIENT FUNCTIONALS OVER THE CLASS OF FUNCTIONS CONVEX IN THE DIRECTION OF THE IMAGINARY AXIS

By Nak Eun Cho, B. Kowalczyk, Adam Lecko. Bulletin of the Australian Mathematical Society, 2019

55 citations recorded by the source corpus.

We apply the Schwarz lemma to find general formulas for the third coefficient of Carathéodory functions dependent on a parameter in the closed unit polydisk. Next we find sharp estimates of the Hankel determinant $H_{2,2}$ and Zalcman functional $J_{2,3}$ over the class ${\mathcal{C}}{\mathcal{V}}$ of analytic functions $f$ normalised such that $\text{Re}\{(1-z^{2})f^{\prime }(z)\}>0$ for $z\in \mathbb{D}:=\{z\in \mathbb{C}:|z|<1\}$ , that is, the subclass of the class of functions convex in the direction of the imaginary axis.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/4caee829df0e0757e92cf0c72255e032019694bb

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In Applied Mathematics

1. Adam Lecko
2. B. Kowalczyk

In Geometry and Topology

1. Adam Lecko
2. B. Kowalczyk

Citations in the corpus

• Second Hankel Determinant of Logarithmic Coefficients of Convex and Starlike Functions of Order Alpha (2021, background): “Further remarks related to extremal functions see [5].”