Third-Order Hankel Determinant for Transforms of the Reciprocal of Bounded Turning Functions

In this paper, we make an attempt to introduce a new subclass of analytic functions. Using the Toeplitz determinants, we obtain the best possible upper bound for the third-order Hankel determinant associated with the $k^{th}$ root transform $[f(z^{k})]^{{1}/{k}}$ of the normalized analytic function $f(z)$ when it belongs to this class, defined on the open unit disc in the complex plane.