jarpm

Format: Online  ISSN 1943-2380

Coefficient Inequality for Uniformly Convex Functions of Order $\alpha$
D. Vamshee Krishna, T. Ram Reddy
Volume 5, Issue 1, 2013    Pages  25 - 41
Received   18 August 2011,   Accepted   23 May 2012
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 the function $f$ and its inverse belonging to the uniformly convex functions of order $\alpha(0\leq\alpha<1)$, using Toeplitz determinants.
Keywords.  Analytic function; Uniformly convex function; Parabolic starlike function; Upper bound; Second Hankel functional; Positive real function; Subordination; Toeplitz determinants.
DOI.  10.5373/jarpm.1080.081811
Full Text:  PDF
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