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arXiv · 2603.10513

On Geometric properties and Coefficient bounds for $\mathcal{S}^*_{B}$

S. Sivaprasad Kumar·Arya Tripathi
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Abstract

This paper deals with the geometric properties of functions belonging to the class $\mathcal{S}^*_{B}$ of starlike functions associated with a balloon-shaped domain, given by \[ \mathcal{S}^{\ast}_{B}= \left\{ f \in \mathcal{A} : \frac{z f'(z)}{f(z)} \prec \frac{1}{1-\log (1+z)} :=B(z), \quad z \in \mathbb{D} \right\}, \] and also derive sharp bounds for the Zalcman functionals, Krushkal inequality, third-order Hankel, Toeplitz and Hermitian-Toeplitz determinant. The sharpness of these results are verified by constructing suitable extremal functions.

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S. Sivaprasad Kumar, Arya Tripathi. 2026-03-11. On Geometric properties and Coefficient bounds for $\mathcal{S}^*_{B}$. https://arxiv.org/abs/2603.10513

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