论文标题
与双曲线有关的全体形态功能家族的系数问题
Coefficients problems for families of holomorphic functions related to hyperbola
论文作者
论文摘要
我们考虑一个与域$ \ mathbb {h}（s）$相关的分析和归一化功能的家族，其中双曲线$ h（s）$作为边界。双曲线$ h（s）$由关系$ \ frac {1}ρ= \ left（2 \ cos \fracφ{s} \ right）^s \ quad（0 <s \ le 1，\ |φ|φ| <（πs）/2 $）。我们主要研究$ zf'/f $或$ 1+zf''/f'$的功能系列的系数问题，将单位磁盘映射到$ \ mathbb {h}（s）$的子集中。我们发现系数范围，解决了Fekete-Szegö问题并估算了Hankel的决定因素。
We consider a family of analytic and normalized functions that are related to the domains $\mathbb{H}(s)$, with a right branch of a hyperbolas $H(s)$ as a boundary. The hyperbola $H(s)$ is given by the relation $\frac{1}ρ=\left( 2\cos\fracφ{s}\right)^s\quad (0<s\le 1,\ |φ|<(πs)/2$). We mainly study a coefficient problem of the families of functions for which $zf'/f$ or $1+zf''/f'$ map the unit disk onto a subset of $\mathbb{H}(s)$. We find coefficients bounds, solve Fekete-Szegö problem and estimate the Hankel determinant.
