论文标题
关于某些分析函数的几何特性
On Geometrical Properties of Certain Analytic functions
论文作者
论文摘要
我们介绍了分析函数类$ \ MATHCAL {f}（ψ）：= \ left \ {f \ in \ Mathcal {a}：\ left（\ frac {zf'（zf'（z）} {f（z）{f（z）} - 1 \ 1 \ right）\ right） ψ（0）= 0 \ right \}，$$，其中$ψ$是无数的，并在$ψ$上建立具有某些几何条件的增长定理，并获得具有一些相关尖锐不平等的Koebe域。请注意，此类的功能可能并非单身。作为应用程序，我们获得了$α$和$β$的增长定理，用于$ \ MATHCAL {BS}（α）（α）的功能中的功能：= \ {f \ in \ Mathcal {a}：（{Zf'（z）}/{z）}/{z）}/{f（z）} - {z）} - 1 \ p peccept { α\在[0,1）\} $和$ \ Mathcal {s} _ {cs}（β）（β）：= \ {f \ in \ Mathcal {a}：{{zf'（zf'（z）}/{f（z）}） - {f（z）}） - 1 \ prec {z}}/}/（z}/（1-1-1-1-1-1-1-1） β\在[0,1）\} $中，分别改善了早期已知的界限。还获得了$ s（\ MATHCAL {BS}（α））$和$ \ Mathcal {BS}（α）$的类的尖锐bohr-radii。还讨论了一些基于几何的例子以及某些新定义的类别。
We introduce the class of analytic functions $$\mathcal{F}(ψ):= \left\{f\in \mathcal{A}: \left(\frac{zf'(z)}{f(z)}-1\right) \prec ψ(z),\; ψ(0)=0 \right\},$$ where $ψ$ is univalent and establish the growth theorem with some geometric conditions on $ψ$ and obtain the Koebe domain with some related sharp inequalities. Note that functions in this class may not be univalent. As an application, we obtain the growth theorem for the complete range of $α$ and $β$ for the functions in the classes $\mathcal{BS}(α):= \{f\in \mathcal{A} : ({zf'(z)}/{f(z)})-1 \prec {z}/{(1-αz^2)},\; α\in [0,1) \}$ and $\mathcal{S}_{cs}(β):= \{f\in \mathcal{A} : ({zf'(z)}/{f(z)})-1 \prec {z}/({(1-z)(1+βz)}),\; β\in [0,1) \}$, respectively which improves the earlier known bounds. The sharp Bohr-radii for the classes $S(\mathcal{BS}(α))$ and $\mathcal{BS}(α)$ are also obtained. A few examples as well as certain newly defined classes on the basis of geometry are also discussed.
