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Coefficient inequality for transforms of parabolic starlike and uniformly convex functions

D. Vamshee Krishna; B. Venkateswarlu; T. RamReddy — 2014

Annales mathématiques Blaise Pascal

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

Third Hankel determinant for starlike and convex functions with respect to symmetric points

D. Vamshee Krishna; B. Venkateswarlu; T. RamReddy — 2016

Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica

The objective of this paper is to obtain best possible upper bound to the $H_{3} (1)$ Hankel determinant for starlike and convex functions with respect to symmetric points, using Toeplitz determinants.

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