arXiv subjects

Arya Tripathi

Publications and source records attributed to Arya Tripathi.

2 recordsLinked to original sources

arXiv2026

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

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.

math.CV↗

arXiv2024

On Coefficient problems for \textbf{$S^*_{\rho}$}

Logarithmic and inverse logarithmic coefficients play a crucial role in the theory of univalent functions. In this study, we focus on the class of starlike functions $\mathcal{S}^*_\rho$, defined as \[ \mathcal{S}^*_\rho = \left\{ f \in \mathcal{A} : \frac{z f'(z)}{f(z)} \prec \rho(z), \; z \in \mathbb{D} \right\}, \] where $\rho(z) := 1 + \sinh^{-1}(z)$, which maps the unit disk $\mathbb{D}$ onto a petal-shaped domain. This investigation aims to establish bounds for the second Hankel and Toeplitz determinants, with their entries determined by the logarithmic coefficients of $f$ and its inverse $f^{-1}$, for functions $f \in \mathcal{S}^*_\rho$.

math.CV↗