论文标题
Janowski Starlike功能
The Booth Lemniscate Starlikeness Radius for Janowski Starlike Functions
论文作者
论文摘要
功能$g_α（z）= 1+ z/（1-αz^2）$，\，$ 0 \ leqα<1 $，将开放单位光盘$ \ mathbb {d} $映射到一个被称为booth lemniscate的域内的内部。与此功能相关联的$G_α$是最近引入的类$ \ Mathcal {bs}（α）$，由$ \ Mathbb {d} $上的正常分析功能$ f $组成，满足了下属$ zf'（z）/f（z）/f（z）/f（z）/f（z）\ precG_α（z）$。有趣的是，它与已知类别的$ \ MATHCAL {m} $在意义上的$ g（z）=（z）=（1/r）f（rz）$属于$ \ mathcal {bs}（α）$ in $（0,1）$中的某些$ r $，并且所有$ r $ in \ in \ mathcal in \ mathcal {m mathcal {m} $。我们发现不同类别的最大半径$ r $ $ \ MATHCAL {M} $，尤其是当$ \ Mathcal {M} $是订单$β$的星形函数或Janowski类别类似Starike函数时。作为此目的的主要工具，我们找到了$g_α（\ mathbb {d}）$中包含的最大光盘的半径，并以某个点$ a \ in \ mathbb {r} $为中心。
The function $G_α(z)=1+ z/(1-αz^2)$, \, $0\leq α<1$, maps the open unit disc $\mathbb{D}$ onto the interior of a domain known as the Booth lemniscate. Associated with this function $G_α$ is the recently introduced class $\mathcal{BS}(α)$ consisting of normalized analytic functions $f$ on $\mathbb{D}$ satisfying the subordination $zf'(z)/f(z) \prec G_α(z)$. Of interest is its connection with known classes $\mathcal{M}$ of functions in the sense $g(z)=(1/r)f(rz)$ belongs to $\mathcal{BS}(α)$ for some $r$ in $(0,1)$ and all $f \in \mathcal{M}$. We find the largest radius $r$ for different classes $\mathcal{M}$, particularly when $\mathcal{M}$ is the class of starlike functions of order $β$, or the Janowski class of starlike functions. As a primary tool for this purpose, we find the radius of the largest disc contained in $G_α(\mathbb{D})$ and centered at a certain point $a \in \mathbb{R}$.
