On the second hankel determinant for the kth-root transform of analytic functions
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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 ?.
2006 ◽
Vol 2006
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pp. 1-6
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2019 ◽
Vol 12
(02)
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pp. 1950017
2013 ◽
Vol 2013
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pp. 1-6
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