On estimation of Hankel determinants for certain class of starlike functions

TL;DR

This paper estimates sharp initial coefficients and Hankel determinants for subclasses of starlike and convex functions associated with a bean-shaped domain, advancing understanding of their geometric properties.

Contribution

It provides new sharp bounds for Hankel determinants and coefficients for specific subclasses of starlike and convex functions related to a bean-shaped domain.

Findings

Sharp bounds for initial coefficients in $ ext{S}_ ext{B}^*$.

Sharp second and third-order Hankel determinants for $ ext{S}_ ext{B}^*$ and $ ext{C}_ ext{B}$.

Enhanced understanding of geometric function classes.

Abstract

In the present study, we consider two subclasses starlike and convex functions, denoted by $\mathcal{S}_{\mathcal{B}}^{*}$ and $\mathcal{C}_{\mathcal{B}}$ respectively, associated with a bean-shaped domain. Further, we estimate certain sharp initial coefficients, as well as second, third and fourth-order Hankel determinants for functions belonging to the class $\mathcal{S}_{\mathcal{B}}^{*}$. Additionally, we compute sharp second and third-order Hankel determinants for functions belonging to the $\mathcal{C}_{\mathcal{B}}$ class.