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

Abstract

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.