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.

Key words and phrases. Analytic function, upper bound, reciprocal of bounded turning function, second Hankel functional, positive real function, Toeplitz determinants.