论文标题
在与双曲余弦功能有关的星形功能的亚家族上
On a subfamily of starlike functions related to Hyperbolic Cosine function
论文作者
论文摘要
我们介绍并研究了一个新的Ma-Minda子类，类似Starlike功能的$ \ Mathcal {s}^*_ {\ varrho}，$定义为$ \ MATHCAL {s}^{*} _ {\ varrho}：= \ left \ {f \ in \ Mathcal {a}：\ frac {zf'（zf'（z）} {f（z）{f（z）} z \ in \ mathbb {d} \ right \}，$$与分析函数$ \ cosh \ sqrt {z}相关联，$，我们选择平方根函数的分支，以便$ \ cosh \ cosh \ sqrt {z} = 1+z/2！+z/2！ $ \ Mathcal {s}^{*} _ {\ varrho} $，并推断出Sharp $ \ Mathcal {S}^{*} _ {\ Varrho} - $ radii，用于某些分析功能的子类别。
We introduce and study a new Ma-Minda subclass of starlike functions $\mathcal{S}^*_{\varrho},$ defined as $$\mathcal{S}^{*}_{\varrho}:=\left\{f\in\mathcal{A}:\frac{zf'(z)}{f(z)} \prec \cosh \sqrt{z}=:\varrho(z), z\in\mathbb{D} \right\},$$ associated with an analytic univalent function $\cosh \sqrt{z},$ where we choose the branch of the square root function so that $\cosh\sqrt{z}=1+z/2!+z^{2}/{4!}+\cdots.$ We establish certain inclusion relations for $\mathcal{S}^{*}_{\varrho}$ and deduce sharp $\mathcal{S}^{*}_{\varrho}-$radii for certain subclasses of analytic functions.
