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# On $H_3(1)$ Hankel determinant for some classes of univalent functions

10/2009;
Source: arXiv

ABSTRACT Focus in this paper is on the Hankel determinant, $H_3(1)$, for the well-known classes of bounded-turning, starlike and convex functions in the open unit disk $E=\{z\in \mathbb{C}\colon|z|<1\}$. The results obtained complete the series of research works in the search for sharp upper bounds on $H_3(1)$ for each of these classes. Comment: 7 pages. To appear as book chapter in "Inequality Theory and Application". Eds: S. S. Dragomir and Y. J. Cho

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##### Article: Upper bound of the third Hankel determinant for a class of analytic functions related with lemniscate of Bernoulli
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ABSTRACT: In this paper, the upper bound of the Hankel determinant H3(1) for a subclass of analytic functions associated with right half of the lemniscate of Bernoulli (x 2 +y 2 ) 2 -2(x 2 -y 2 )=0 is investigated.
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