Sharp Estimates of Hankel Determinants for certain classes of convex univalent functions
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866913042270257152 |
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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 $f$ 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 $\mathcal{C}(φ)$ defined as $\mathcal{C}(φ) := \left\{ f \in \mathcal{A} : 1+zf''(z)/f'(z) \prec φ(z):=1+z+ m/n\, \, z^2, \text{ with } 2m \le n,\text{ for } m, n \in \mathbb{N} \right\},$ and compute the sharp second and third Hankel determinants for the functions in $\mathcal{C}(φ)$. Furthermore, we determine the extremal functions for the sharp estimates of the Hankel determinants. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2604_16833 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Sharp Estimates of Hankel Determinants for certain classes of convex univalent functions Allu, Vasudevarao Kumar, Shobhit Complex Variables 30C45, 30C50, 41A10 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 $\mathcal{C}(φ)$ defined as $\mathcal{C}(φ) := \left\{ f \in \mathcal{A} : 1+zf''(z)/f'(z) \prec φ(z):=1+z+ m/n\, \, z^2, \text{ with } 2m \le n,\text{ for } m, n \in \mathbb{N} \right\},$ and compute the sharp second and third Hankel determinants for the functions in $\mathcal{C}(φ)$. Furthermore, we determine the extremal functions for the sharp estimates of the Hankel determinants. |
| title | Sharp Estimates of Hankel Determinants for certain classes of convex univalent functions |
| topic | Complex Variables 30C45, 30C50, 41A10 |
| url | https://arxiv.org/abs/2604.16833 |