论文标题
具有非变化多项式的Starlike函数产物的星光度
Starlikeness of a product of starlike functions with non-vanishing polynomials
论文作者
论文摘要
对于功能$ f $ star的订单$α$，$ 0 \leqslantα<1 $，一种非恒定的多项式$ q $ $ n $的$ n $的$ q $ q $ n $，在单位盘$ \ mathbb {d} $和$β> 0 $中，我们考虑函数$ f：\ mathbb {d} $F(z)=f(z) (Q(z))^{β/n}$ and find the largest value of $r\in (0,1]$ such that $r^{-1} F(rz)$ lies in various known subclasses of starlike functions such as the class of starlike functions of order $λ$, the classes of starlike functions associated with the exponential function, cardioid, a rational function,肾脏区域和改良的乙状结肠功能。
For a function $f$ starlike of order $α$, $0\leqslant α<1$, a non-constant polynomial $Q$ of degree $n$ which is non-vanishing in the unit disc $\mathbb{D}$ and $β>0$, we consider the function $F:\mathbb{D}\to\mathbb{C}$ defined by $F(z)=f(z) (Q(z))^{β/n}$ and find the largest value of $r\in (0,1]$ such that $r^{-1} F(rz)$ lies in various known subclasses of starlike functions such as the class of starlike functions of order $λ$, the classes of starlike functions associated with the exponential function, cardioid, a rational function, nephroid domain and modified sigmoid function. Our radii results are sharp. We also discuss the correlation with known radii results as special cases.
