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 $\mathcal{S}_{\mathcal{B}}^{*}$ 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.