On Third-Order Determinant Bounds for the class $\mathcal{S}^*_{B}$
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866910049101676544 |
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| author | Kumar, S. Sivaprasad Tripathi, Arya |
| author_facet | Kumar, S. Sivaprasad Tripathi, Arya |
| contents | This paper deals with sharp bounds for the third-order Hankel, Toeplitz and Hermitian-Toeplitz determinant of functions belonging to the class $\mathcal{S}^*_{B}$ of starlike functions associated with a balloon-shaped domain, given by \[
\mathcal{S}^{\ast}_{B}= \left\{ f \in \mathcal{A} : \frac{z f'(z)}{f(z)} \prec \frac{1}{1-\log (1+z)} :=B(z), \quad z \in \mathbb{D} \right\}.
\] By applying coefficient inequalities and properties of these functions, we obtain sharp bounds for these determinants. The sharpness of the results is verified by constructing suitable extremal functions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_10513 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On Third-Order Determinant Bounds for the class $\mathcal{S}^*_{B}$ Kumar, S. Sivaprasad Tripathi, Arya Complex Variables This paper deals with sharp bounds for the third-order Hankel, Toeplitz and Hermitian-Toeplitz determinant of functions belonging to the class $\mathcal{S}^*_{B}$ of starlike functions associated with a balloon-shaped domain, given by \[ \mathcal{S}^{\ast}_{B}= \left\{ f \in \mathcal{A} : \frac{z f'(z)}{f(z)} \prec \frac{1}{1-\log (1+z)} :=B(z), \quad z \in \mathbb{D} \right\}. \] By applying coefficient inequalities and properties of these functions, we obtain sharp bounds for these determinants. The sharpness of the results is verified by constructing suitable extremal functions. |
| title | On Third-Order Determinant Bounds for the class $\mathcal{S}^*_{B}$ |
| topic | Complex Variables |
| url | https://arxiv.org/abs/2603.10513 |