Best bounds for the second Hankel determinant of the kth-root transform of analytic functions

Let f be a normalized analytic function in the open unit disk of the complex plane satisfying 1 + zf″(z) / f′(z) is subordinate to a given analytic function. For this function, the best bound is obtained for the second Hankel determinant of the th-root transform z[f(zk)/zk]1k. Connections are also made to earlier known results.