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arXiv · 2604.16833

Sharp Estimates of Hankel Determinants for certain classes of convex univalent functions

Vasudevarao Allu·Shobhit Kumar
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Abstract

Let $\mathcal{A}$ denote the class of analytic functions $f$ such that $f(0)=0$ and $f'(0)=1$ in the unit disk $\mathbb{D}:=\{z \in \mathbb{C}: |z|<1\}.$ We examine the properties of the class $\mathcal{C}(\varphi)$ defined as $\mathcal{C}(\varphi) := \left\{ f \in \mathcal{A} : 1+zf''(z)/f'(z) \prec \varphi(z):=1+z+ m/n\, \, z^2, \text{ with } 2m \le n,\text{ for } m, n \in \mathbb{N} \right\},$ and compute the sharp second and third Hankel determinants for the functions in $\mathcal{C}(\varphi)$. Furthermore, we determine the extremal functions for the sharp estimates of the Hankel determinants.

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Vasudevarao Allu, Shobhit Kumar. 2026-04-18. Sharp Estimates of Hankel Determinants for certain classes of convex univalent functions. https://arxiv.org/abs/2604.16833

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