Coefficient inequality for transforms of reciprocal
of bounded turning functions

Abstract. In the present paper we introduce a new subclass of analytic functions. We prove a sharp upper bound to the second Hankel determinant associated with the \(k^{th}q\) root transform \(\left[ f(z ^k ) \right] ^{\frac{1}{k}}\) of the normalized analytic function \(f(z)\), when it belongs to this class, using Toeplitz determinants.