Coefficient inequality for transforms of parabolic starlike and uniformly convex functions

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

doi:10.5802/ambp.341

Vamshee Krishna, D.¹ ; Venkateswarlu, B.¹ ; RamReddy, T.²

¹ Department of Mathematics GIT, GITAM University Visakhapatnam- 530 045, A.P., India.
² Department of Mathematics, Kakatiya University, Warangal- 506 009, A.P., India.

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

Résumé

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.

DOI : 10.5802/ambp.341

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

Affiliations des auteurs :

Vamshee Krishna, D. ¹ ; Venkateswarlu, B. ¹ ; RamReddy, T. ²

¹ Department of Mathematics GIT, GITAM University Visakhapatnam- 530 045, A.P., India.
² Department of Mathematics, Kakatiya University, Warangal- 506 009, A.P., India.

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     title = {Coefficient inequality for transforms of parabolic starlike and uniformly convex functions},
     journal = {Annales math\'ematiques Blaise Pascal},
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Vamshee Krishna, D.; Venkateswarlu, B.; RamReddy, T. Coefficient inequality for transforms of parabolic starlike and uniformly convex functions. Annales mathématiques Blaise Pascal, Tome 21 (2014) no. 2, pp. 39-56. doi : 10.5802/ambp.341. http://www.numdam.org/articles/10.5802/ambp.341/

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