Some application of Grunsky coefficients in the theory of univalent functions

Milutin Obradović; Nikola Tuneski

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arXiv · 2009.11945

Some application of Grunsky coefficients in the theory of univalent functions

Milutin Obradović·Nikola Tuneski

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Abstract

Let function $f$ be normalized, analytic and univalent in the unit disk ${\mathbb D}=\{z:|z|<1\}$ and $f(z)=z+\sum_{n=2}^{\infty} a_n z^n$. Using a method based on Grusky coefficients we study several problems over that class of univalent functions: upper bounds of the special case of the generalised Zalcman conjecture $|a_2a_3-a_4|$, of the third logarithmic coefficient, and of the second Hankel determinant for the logarithmic coefficients.

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Milutin Obradović, Nikola Tuneski. 2020-09-24. Some application of Grunsky coefficients in the theory of univalent functions. https://arxiv.org/abs/2009.11945

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