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arXiv · 2411.13102

Improvements of certain results of the class $\mathcal{S}$ of univalent functions

Milutin Obradović·Nikola Tuneski
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Abstract

For $f\in \mathcal{S}$, the class univalent functions in the unit disk $\mathbb{D}$ and given by $f(z)=z+\sum_{n=2}^{\infty} a_n z^n$ for $z\in \mathbb{D}$, we improve previous bounds for the second and third Hankel determinants in case when either $a_2=0,$ or $a_3=0$. We also improve an upper bound for the coefficient difference $|a_4|-|a_3|$ when $f\in \mathcal{S}$.

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Milutin Obradović, Nikola Tuneski. 2024-11-20. Improvements of certain results of the class $\mathcal{S}$ of univalent functions. https://arxiv.org/abs/2411.13102

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