论文标题
Janowski凸功能的Schwarzian规范估计
The Schwarzian norm estimates for Janowski convex functions
论文作者
论文摘要
对于$ -1 \ leq b <a \ leq 1 $，让$ \ mathcal {c}（a，a，b）$表示在单位盘$ \ mathbb {d}中定义的标准化的janowski convex函数的类别$ 1+zf''（z）/f'（z）\ prec（1+az）/（1+bz）$。在本文中，我们确定了Schwarzian Narm的尖锐估计，用于类$ \ Mathcal {C}（a，b）$中的功能。 Dieudonné的引理在有限函数的点上给出了衍生物的确切区域，在这项研究中起着关键作用，我们还使用这种引理来通过一种新方法来构建极端功能。
For $-1\leq B<A\leq 1$, let $\mathcal{C}(A,B)$ denote the class of normalized Janowski convex functions defined in the unit disk $\mathbb{D}:=\{z\in\mathbb{C}:|z|<1\}$ that satisfy the subordination relation $1+zf''(z)/f'(z)\prec (1+Az)/(1+Bz)$. In the present article, we determine the sharp estimate of the Schwarzian norm for functions in the class $\mathcal{C}(A,B)$. The Dieudonné's lemma which gives the exact region of variability for derivatives at a point of bounded functions, plays the key role in this study, and we also use this lemma to construct the extremal functions for the sharpness by a new method.
