论文标题
$ H_3（1）$的猜想，用于某些Starlike功能
A Conjecture on $H_3(1)$ For Certain Starlike Functions
论文作者
论文摘要
我们证明了关于第三个汉克尔决定因素的猜想，该决定因素是``肛门''。数学。物理学，https：//doi.org/10.1007/s13324-021-00483-7“，它指出$ | h_3（1）| \ leq 1/9 $对于类$ \ Mathcal {s} _} _ {s} _ {\ wp} _ {\ wp}^{ φ（z）：= 1+ze^z \} $。还获得了$ \ MATHCAL {S}^*（φ）Starlike功能的$。
We prove a conjecture concerning the third Hankel determinant, proposed in ``Anal. Math. Phys., https://doi.org/10.1007/s13324-021-00483-7", which states that $|H_3(1)|\leq 1/9$ is sharp for the class $\mathcal{S}_{\wp}^{*}=\{zf'(z)/f(z) \prec φ(z):=1+ze^z\}$. In addition, we also establish bounds for sixth and seventh coefficient, and $|H_4(1)|$ for functions in $\mathcal{S}_{\wp}^{*}$. The general bounds for two and three-fold symmetric functions related to the Ma-Minda classes $\mathcal{S}^*(φ)$ of starlike functions are also obtained.
