论文标题
尖锐的Bohr半径常数用于某些分析功能
Sharp Bohr Radius Constants For Certain Analytic Functions
论文作者
论文摘要
$ \ MATHCAL {G} $组成的BOHR RADIUS $ f（z）= \ sum_ {n = 0}^{\ infty} a_nz^n $在单位盘$ \ mathbb {d} = \ in \ in \ mathbb in \ mathbb { $ f $ in Class $ \ MATHCAL {G} $满足不等式\ begin {equination*} d \ left（\ sum_ {n = 0}^{\ infty} | a_nz^n |，| f（| f（| f） \ partial f（\ mathbb {d}））\ end {equation*}对于所有$ | z | = r \ leq r^*$，其中$ d $是欧几里得距离。在本文中，我们的目的是确定满足差异下属关系的分析功能的类别的BOHR半径$ f $ $ zf'（z）/f（z）/f（z）\ pROC H（z）$和$ f（z）+βz+βzf'（z）+γz+γz+γz+γz^2 f'（z）'（z）'（z）\ prec h（z）\ prec h（z）\ prec h（z）$ h $ h $ h $ h $ h $ h $ h $ h jan askki jan ski功能。对于$α$ -CONVEX函数和通常的实际功能，获得了类似的结果。所有获得的结果都很清晰。
The Bohr radius for a class $\mathcal{G}$ consisting of analytic functions $f(z)=\sum_{n=0}^{\infty}a_nz^n$ in unit disc $\mathbb{D}=\{z\in\mathbb{C}:|z|<1\}$ is the largest $r^*$ such that every function $f$ in the class $\mathcal{G}$ satisfies the inequality \begin{equation*} d\left(\sum_{n=0}^{\infty}|a_nz^n|, |f(0)|\right) = \sum_{n=1}^{\infty}|a_nz^n|\leq d(f(0), \partial f(\mathbb{D})) \end{equation*} for all $|z|=r \leq r^*$, where $d$ is the Euclidean distance. In this paper, our aim is to determine the Bohr radius for the classes of analytic functions $f$ satisfying differential subordination relations $zf'(z)/f(z) \prec h(z)$ and $f(z)+βz f'(z)+γz^2 f''(z)\prec h(z)$, where $h$ is the Janowski function. Analogous results are obtained for the classes of $α$-convex functions and typically real functions, respectively. All obtained results are sharp.
