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Proyecciones (Antofagasta)

Print version ISSN 0716-0917

Proyecciones (Antofagasta) vol.37 no.2 Antofagasta June 2018 


Bound on H3(1) Hankel determinant for pre-starlike functions of order α

D. Vamshee Krishna1 

D. Shalini2 

1GITAM University, Department of Mathematics, Visakhapatnam 530 045, A. P., India. E-mail :

2Sri Venkateswara College of Engineering and Technology, Affiliated to JNTUK, Department of Mathematics, Etcherla 532 410, A. P., India. E-mail :


The objective of this paper is to obtain best possible upper bound to the third Hankel determinant for the pre-starlike functions of order α(0≤α<1), using Toeplitz determinants.

Keywords and phrases : Analytic function; pre-starlike function; convex function; upper bound; second and third Hankel functionals; positive real function; convolution; Toeplitz determinants

2010 Mathematics Subject Classification: 30C45; 30C50.

Texto completo disponible sólo en PDF.

Full text available only in PDF format.

Acknowledgements :

The authors thank Prof. T. RamReddy for useful discussion and suggestions. The authors also express their sincere thanks to the Editor and the esteemed Referees for their valuable suggestions to improve the manuscript.


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Received: September 2017; Accepted: March 2018

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