The second and third Hankel determinants for starlike MA--Minda subclass associated to quadratic polynomials
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866911581783195648 |
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| author | Allu, Vasudevarao Kumar, Shobhit |
| author_facet | Allu, Vasudevarao Kumar, Shobhit |
| contents | 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 $\mathcal{S}^*(φ):=\{f\in\mathcal{A}:{zf'(z)}/{f(z)}\prec φ(z):=1+z+{m}/{n}\,\, z^2,\text{ such that } 2m \le n, \text{ where } m,n\in\mathbb{N}\}.$ Furthermore, we show that the bounds are sharp by determining the extremal functions for the Hankel determinants. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_09266 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The second and third Hankel determinants for starlike MA--Minda subclass associated to quadratic polynomials Allu, Vasudevarao Kumar, Shobhit Complex Variables 30C45, 30C50, 41A10 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 $\mathcal{S}^*(φ):=\{f\in\mathcal{A}:{zf'(z)}/{f(z)}\prec φ(z):=1+z+{m}/{n}\,\, z^2,\text{ such that } 2m \le n, \text{ where } m,n\in\mathbb{N}\}.$ Furthermore, we show that the bounds are sharp by determining the extremal functions for the Hankel determinants. |
| title | The second and third Hankel determinants for starlike MA--Minda subclass associated to quadratic polynomials |
| topic | Complex Variables 30C45, 30C50, 41A10 |
| url | https://arxiv.org/abs/2604.09266 |