The second and third Hankel determinants for certain classes of functions
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866913024212729856 |
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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 consider $\mathcal{S}^*(φ) := \left\{ f \in \mathcal{A} : zf'(z)/f(z) \prec φ(z):=(1+z/2)^2 \right\}$, a subclass of starlike functions and we compute the sharp second and third Hankel determinants for the functions in $\mathcal{S}^*(φ)$. Furthermore, we determine the extremal functions for the coefficient bounds of the functions belonging to $\mathcal{S}^*(φ)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_10298 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The second and third Hankel determinants for certain classes of functions Allu, Vasudevarao Kumar, Shobhit Complex Variables 30C45, 30C50 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 consider $\mathcal{S}^*(φ) := \left\{ f \in \mathcal{A} : zf'(z)/f(z) \prec φ(z):=(1+z/2)^2 \right\}$, a subclass of starlike functions and we compute the sharp second and third Hankel determinants for the functions in $\mathcal{S}^*(φ)$. Furthermore, we determine the extremal functions for the coefficient bounds of the functions belonging to $\mathcal{S}^*(φ)$. |
| title | The second and third Hankel determinants for certain classes of functions |
| topic | Complex Variables 30C45, 30C50 |
| url | https://arxiv.org/abs/2604.10298 |