Tbilisi Mathematical Journal

Hankel determinant for starlike and convex functions of order alpha

D. Vamshee Krishna and T. Ramreddy

Full-text: Open access

Abstract

The objective of this paper is to obtain an upper bound to the second Hankel determinant $|a_{2}a_{4}-a_{3}^{2}|$ for starlike and convex functions of order $\alpha$ $(0\leq\alpha\lt1)$, also for the inverse function of $f$, belonging to the class of convex functions of order $\alpha$, using Toeplitz determinants.

Article information

Source
Tbilisi Math. J., Volume 5, Issue 1 (2012), 65-76.

Dates
Received: 21 October 2011
Revised: 11 October 2012
Accepted: 29 October 2012
First available in Project Euclid: 12 June 2018

Permanent link to this document
https://projecteuclid.org/euclid.tbilisi/1528768890

Mathematical Reviews number (MathSciNet)
MR3006759

Zentralblatt MATH identifier
1279.30017

Subjects
Primary: 30C45: Special classes of univalent and multivalent functions (starlike, convex, bounded rotation, etc.)
Secondary: 30C50: Coefficient problems for univalent and multivalent functions

Keywords
Analytic function starlike and convex functions upper bound second Hankel functional positive real function Toeplitz determinants

Citation

Krishna, D. Vamshee; Ramreddy, T. Hankel determinant for starlike and convex functions of order alpha. Tbilisi Math. J. 5 (2012), no. 1, 65--76. https://projecteuclid.org/euclid.tbilisi/1528768890


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