Two applications of Grunsky coefficients in the theory of univalent functions

Milutin Obradović; Nikola Tuneski

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arXiv · 2201.07336

Two applications of Grunsky coefficients in the theory of univalent functions

Milutin Obradović·Nikola Tuneski

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Abstract

Let $\mathcal{S}$ denote the class of functions $f$ which are analytic and univalent in the unit disk ${\mathbb D}=\{z:|z|<1\}$ and normalized with $f(z)=z+\sum_{n=2}^{\infty} a_n z^n$. Using a method based on Grusky coefficients we study two problems over the class $\mathcal{S}$: estimate of the fourth logarithmic coefficient and upper bound of the coefficient difference $|a_5|-|a_4|$.

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Milutin Obradović, Nikola Tuneski. 2022-01-14. Two applications of Grunsky coefficients in the theory of univalent functions. https://arxiv.org/abs/2201.07336

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