In this paper we obtain the bound of the third Hankel determinant

$$\begin{aligned} H_3(1) = \left| \begin{array}{c@{\quad }c@{\quad }c} 1 &{} a_2&{} a_3\\ a_2 &{} a_3&{} a_4\\ a_3 &{} a_4&{} a_5\\ \end{array} \right| \end{aligned}$$

for the class \({\mathcal {S}}^*\) of univalent starlike functions, i.e. the functions which satisfy in the unit disk the condition \({{\,\mathrm{Re}\,}}\frac{zf'(z)}{f(z)}>0\). In our research we apply the correspondence between starlike functions and Schwarz functions and the results obtained by Prokhorov and Szynal and by Carlson.

中文翻译：

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单价星形函数的第三个Hankel行列式

在本文中，我们获得了第三汉克尔行列式的界

$$ \ begin {aligned} H_3（1）= \ left | \ begin {array} {c @ {\ quad} c @ {\ quad} c} 1＆{} a_2＆{} a_3 \\ a_2＆{} a_3＆{} a_4 \\ a_3＆{} a_4＆{} a_5 \\ \ end {array} \ right | \ end {aligned} $$

对于单价星形函数的类\（{{mathcal {S}} ^ * \），即在单位磁盘中满足条件\（{{\，\ mathrm {Re} \，}} \ frac { zf'（z）} {f（z）}> 0 \）。在我们的研究中，我们应用了星形函数和Schwarz函数之间的对应关系以及Prokhorov和Szynal以及Carlson获得的结果。