论文标题
BOHR半径，用于某些类别的二星和凸出功能
Bohr radius for certain classes of starlike and convex univalent functions
论文作者
论文摘要
我们说，由分析函数组成的类$ \ Mathcal {f} $ $ f（z）= \ sum_ {n = 0}^{\ infty} a_ {n} z^{n} z^{n} $在单位磁盘disk $ \ \ mathbb {d}中现象是否存在$ r_ {f} \ in（0,1）$，这样$$ \ sum_ {n = 1}^{\ infty} | a_ {n} z^{n} | \ leq d（f（f（0），\ partial f（\ partial f（\ mathbb {d}）$$对于每个函数$ f \ in \ mathcal in \ mathcal {f} 距离。最大的半径$ r_ {f} $是类$ \ mathcal {f} $的Bohr半径。在本文中，我们建立了由Ma-Minda型Starlike功能和Ma-Minda型凸功能以及相对于边界点的Starlike函数类别的类别组成的类别的BOHR现象。
We say that a class $\mathcal{F}$ consisting of analytic functions $f(z)=\sum_{n=0}^{\infty} a_{n}z^{n}$ in the unit disk $\mathbb{D}:=\{z\in \mathbb{C}: |z|<1\}$ satisfies a Bohr phenomenon if there exists $r_{f} \in (0,1)$ such that $$ \sum_{n=1}^{\infty} |a_{n}z^{n}|\leq d(f(0),\partial f(\mathbb{D})) $$ for every function $f \in \mathcal{F}$ and $|z|=r\leq r_{f}$, where $d$ is the Euclidean distance. The largest radius $r_{f}$ is the Bohr radius for the class $\mathcal{F}$. In this paper, we establish the Bohr phenomenon for the classes consisting of Ma-Minda type starlike functions and Ma-Minda type convex functions as well as for the class of starlike functions with respect to a boundary point.
