论文标题
某些近风函数的Starlikeness
Starlikeness for Certain Close-to-Star Functions
论文作者
论文摘要
我们发现订单$α$，$ 0 \ leqα<1 $的星空的半径是正常化的分析功能$ f $在单位磁盘上满足$ \ permatatorName {re}（f（z）/g（z）/g（z））> 0 $或$ \ weft | （f（z）/g（z）） - 1 \ right | <1 $，对于某些近距离 - 明星函数$ g $，带有$ \ operatatorName {re}（g（z）/（z+z^2/2））> 0 $以及近点的近点函数$ f $ f $ f $ f $ f $ fop $ f $ f $满足$ \ \ operation $ \ operateRonnAme {re} $} $ {z f（z）（z）/（z）/（z）/（z）/（z）/（z）/（z）/（z）/（z）/（z）^++^+^2/2/（z）/（z）/（z）^+++。其他几个半径，例如单位性和抛物线抛物性的半径，与适当秩序的星光般的半径相同。
We find the radius of starlikeness of order $α$, $0\leq α<1$, of normalized analytic functions $f$ on the unit disk satisfying either $\operatorname{Re}(f(z)/g(z))>0$ or $\left| (f(z)/g(z))-1\right|<1$ for some close-to-star function $g$ with $\operatorname{Re}(g(z)/(z+z^2/2))>0$ as well as of the class of close-to-star functions $f$ satisfying $\operatorname{Re}(f(z)/(z+z^2/2))>0$. Several other radii such as radius of univalence and parabolic starlikeness are shown to be the same as the radius of starlikeness of appropriate order.
