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.
Keywords:analytic function, upper bound,
reciprocal of a bounded turning function,
third Hankel functional, positive real function,
Toeplitz determinants.
