On estimation of Hankel determinants for certain class of starlike functions

In the present study, we consider two subclasses starlike and convex functions, denoted by ${\mathcal{S}}_{\mathcal{B}}^{\ast }$ 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 ${\mathcal{S}}_{\mathcal{B}}^{\ast }$. Additionally, we compute sharp second and third-order Hankel determinants for functions belonging to the ${\mathcal{C}}_{\mathcal{B}}$ class.