Certain Coefficient Problems of ${\mathcal{S}}_e^{\ast }$ and ${\mathcal{C}}_e$

In this current study, we consider the classes ${\mathcal{S}}_e^{\ast }$ and ${\mathcal{C}}_e$ to obtain sharp bounds for the third Hankel determinant for functions within these classes. Additionally, we provide estimates for the sixth and seventh coefficients while establishing the fourth-order Hankel determinant as well.