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arXiv · 2604.09266

The second and third Hankel determinants for starlike MA--Minda subclass associated to quadratic polynomials

Vasudevarao Allu·Shobhit Kumar
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Abstract

Let $\mathcal{A}$ denote the class of analytic functions such that $f(0)=0$ and $f'(0)=1$ in the unit disk $\mathbb{D}:=\{z \in \mathbb{C}: |z|<1\}$. In this paper, we discuss the properties of a starlike subclass and compute its second and third Hankel determinants; where the class is defined as $\mathcal{S}^*(\varphi):=\{f\in\mathcal{A}:{zf'(z)}/{f(z)}\prec \varphi(z):=1+z+{m}/{n}\,\, z^2,\text{ such that } 2m \le n, \text{ where } m,n\in\mathbb{N}\}.$ Furthermore, we show that the bounds are sharp by determining the extremal functions for the Hankel determinants.

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Vasudevarao Allu, Shobhit Kumar. 2026-04-10. The second and third Hankel determinants for starlike MA--Minda subclass associated to quadratic polynomials. https://arxiv.org/abs/2604.09266

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