论文标题
某些单价功能子类的可变性区域
Region of variability for certain subclass of univalent functions
论文作者
论文摘要
令$ \ mathbb {d}：= \ {z \ in \ mathbb {c}：| z | <1 \} $为单位磁盘。对于$ 0 <α<1 $，让$f_α（z）= z/（1-z^α）$ for \ z \ in \ mathbb {d} $。我们考虑分析函数的类$ \ Mathcal {f} $ $f_α$满足$ \ re \ left（1+zf“_α（z）/f'_α（z）/f'_α（z）\ right）>β$ for $ 0 <β<1 $。当$ f $时，\ mathbb {d} $在类别$ {\ Mathcal f}（λ）上有所不同，= \ {f_α\ in \ Mathcal {f}：f_α（0）= 0，f'_α（f'_α（0）= 1 \ mbox {for} \，\，0 \leqλ\ leq 1 \} $。
Let $\mathbb{D}:=\{z\in \mathbb{C}: |z|<1\}$ be the unit disk. For $0<α<1$, let $f_α(z)=z/(1-z^α)$ for $z \in \mathbb{D}$. We consider the class $\mathcal{F}$ of analytic functions $f_α$ which satisfy $\Re \left(1+zf"_α(z)/f'_α(z)\right) > β$ for $0<β<1$. In this paper, we determine the region of variability of $\log f'_α(z_0)$ for fixed $z_{0} \in \mathbb{D}$ when $f$ varies over the class ${\mathcal F}(λ):=\{f_α \in \mathcal{F}: f_α(0)=0, f'_α(0)=1 \, \mbox{and} \, f"_α(0)=2λ(1-β) \,\,\, \mbox{for} \,\, 0\leq λ\leq 1\}$.
