THE SHARP BOUND FOR THE HANKEL DETERMINANT OF THE THIRD KIND FOR CONVEX FUNCTIONS
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DOI: 10.1017/s0004972717001125
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| read more here.
Keywords: bound hankel; sharp bound; hankel determinant; convex functions ... See more keywords