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THE SHARP BOUND FOR THE HANKEL DETERMINANT OF THE THIRD KIND FOR CONVEX FUNCTIONS.
- Source :
-
Bulletin of the Australian Mathematical Society . Jun2018, Vol. 97 Issue 3, p435-445. 11p. - Publication Year :
- 2018
-
Abstract
- We prove the sharp inequality $|H_{3,1}(f)|\leq 4/135$ for convex functions, that is, for analytic functions $f$ with $a_{n}:=f^{(n)}(0)/n!,~n\in \mathbb{N}$ , such that $$\begin{eqnarray}Re\bigg\{1+\frac{zf^{\prime \prime }(z)}{f^{\prime }(z)}\bigg\}>0\quad \text{for}~z\in \mathbb{D}:=\{z\in \mathbb{C}:|z| where $H_{3,1}(f)$ is the third Hankel determinant $$\begin{eqnarray}H_{3,1}(f):=\left|\begin{array}{@{}ccc@{}}a_{1} & a_{2} & a_{3}\\ a_{2} & a_{3} & a_{4}\\ a_{3} & a_{4} & a_{5}\end{array}\right|.\end{eqnarray}$$ [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00049727
- Volume :
- 97
- Issue :
- 3
- Database :
- Academic Search Index
- Journal :
- Bulletin of the Australian Mathematical Society
- Publication Type :
- Academic Journal
- Accession number :
- 129620622
- Full Text :
- https://doi.org/10.1017/S0004972717001125