Abstract
Let f be a normalized analytic function in the open unit disk of the complex
plane satisfying zf'(z)/f(z) is subordinate to a given analytic function
?. A sharp bound is obtained for the second Hankel determinant of the
kth-root transform z[f(zk)/zk]1/k. Best bounds for the Hankel
determinant are also derived for the kth-root transform of several other
classes, which include the class of ?-convex functions and ?-logarithmically
convex functions. These bounds are expressed in terms of the coefficients of
the given function ?, and thus connect with earlier known results for
particular choices of ?.
nema