Coefficient inequality for transforms of parabolic starlike and uniformly convex functions

Vamshee Krishna, D.; Venkateswarlu, B.; RamReddy, T.

Annales mathématiques Blaise Pascal, Tome 21 (2014) no. 2, pp. 39-56.

The objective of this paper is to obtain sharp upper bound to the second Hankel functional associated with the $k^{th}$ root transform ${\left[f\left(z^k\right)\right]}^{\frac{1}{k}}$ of normalized analytic function $f\left(z\right)$ belonging to parabolic starlike and uniformly convex functions, defined on the open unit disc in the complex plane, using Toeplitz determinants.

Classification : 30C45, 30C50
Mots clés : Analytic function, parabolic starlike and uniformly convex functions, upper bound, second Hankel functional, positive real function, Toeplitz determinants.

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