论文标题
有心脏域和类似星形的功能
A Cardioid Domain and Starlike Functions
论文作者
论文摘要
我们介绍并研究了一类类似星光的函数，由\ begin {equation*} \ mathscr {s}^*_ \ wp：= \ left \ {f \ in \ mathcal {a}：\ frac {zf {zf'（z）}} {f（z）} {f（z）} {z） \ end {equation*}其中$ \ wp $将单元磁盘映射到有氧域上。我们发现$ \ wp（z）$的凸度半径，并建立$ \ mathscr {s}^*_ \ wp $与一些知名类之间的包含关系。此外，我们得出了$ \ Mathscr {s}^*_ \ wp $的类别的半径常数和系数相关的结果。
We introduce and study a class of starlike functions defined by \begin{equation*} \mathscr{S}^*_\wp:=\left\{f\in\mathcal{A}: \frac{zf'(z)}{f(z)}\prec 1+ze^z=:\wp(z)\right\}, \end{equation*} where $\wp$ maps the unit disk onto a cardioid domain. We find the radius of convexity of $\wp(z)$ and establish the inclusion relations between the class $ \mathscr{S}^*_\wp$ and some well-known classes. Further we derive sharp radius constants and coefficient related results for the class $ \mathscr{S}^*_\wp$.
