The second and third Hankel determinants for certain convex subclass of functions
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866913024231604224 |
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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 the present paper, we consider $\mathcal{C}(φ) := \left\{ f \in \mathcal{A} : 1+zf''(z)/f'(z) \prec φ(z):=(1+z/2)^2 \right\}$, as subclass of convex functions and compute the sharp second and third Hankel determinants for functions in $\mathcal{C}(φ)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_10301 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The second and third Hankel determinants for certain convex subclass 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 the present paper, we consider $\mathcal{C}(φ) := \left\{ f \in \mathcal{A} : 1+zf''(z)/f'(z) \prec φ(z):=(1+z/2)^2 \right\}$, as subclass of convex functions and compute the sharp second and third Hankel determinants for functions in $\mathcal{C}(φ)$. |
| title | The second and third Hankel determinants for certain convex subclass of functions |
| topic | Complex Variables 30C45, 30C50 |
| url | https://arxiv.org/abs/2604.10301 |