On estimation of Hankel determinants for certain class of starlike functions

Abstract: In the present study, we consider two subclasses starlike and convex functions, denoted by $\mathcal{S}<em>{\mathcal{B}}<sup>{*}$ and $\mathcal{C}</em>{\mathcal{B}}$ 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 $\mathcal{S}<em>{\mathcal{B}}<sup>{*}$. Additionally, we compute sharp second and third-order Hankel determinants for functions belonging to the $\mathcal{C}</em>{\mathcal{B}}$ class.