On Geometric properties and Coefficient bounds for ${\mathcal{S}}_B^{\ast }$

This paper deals with the geometric properties of functions belonging to the class ${\mathcal{S}}_B^{\ast }$ of starlike functions associated with a balloon-shaped domain, given by $${\mathcal{S}}_B^{\ast }=\{f\in \mathcal{A}:\frac{z{f}^{\mathrm{\prime }}(z)}{f(z)}\prec \frac{1}{1-\log (1+z)}:=B(z),z\in \mathbb{D}\},$$ and also derive sharp bounds for the Zalcman functionals, Krushkal inequality, third-order Hankel, Toeplitz and Hermitian-Toeplitz determinant. The sharpness of these results are verified by constructing suitable extremal functions.