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arXiv · 2112.15449

Certain properties of the class of univalent functions with real coefficients

Milutin Obradović·Nikola Tuneski
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Abstract

Let ${\mathcal U}^+$ be the class of analytic functions $f$ such that $\frac{z}{f(z)}$ has real and positive coefficients and $f^{-1}$ be its inverse. In this paper we give sharp estimates of the initial coefficients and initial logarithmic coefficients for $f$, as well as, sharp estimates of the second and the third Hankel determinant for $f$ and $f^{-1}$. We also show that the Zalcman conjecture holds for functions $f$ from ${\mathcal U}^+$.

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Milutin Obradović, Nikola Tuneski. 2021-12-29. Certain properties of the class of univalent functions with real coefficients. https://arxiv.org/abs/2112.15449

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