AI 中文总结
该研究针对单位圆盘内由特定曲线界定区域从属关系定义的单叶星形函数子类，求得了高阶Schippers-Schwarzian导数的精确上界及对应极值函数，并将其应用于Grunsky系数精确界的推导。
AI 中文摘要
针对单位圆盘内多个单叶星形函数子类，我们求得了初始高阶Schippers-Schwarzian导数σ₃(f)(0)和σ₄(f)(0)的精确上界。这些子类中的函数由对指数正弦曲线、心脏线或花瓣形曲线围成的区域的从属关系定义。我们确定了这些子类中每个不变量的精确界，并找到了对应的极值函数。作为应用，我们还得到了初始Grunsky系数ω₁,₁和ω₁,₂的精确界。
英文摘要
We find sharp upper bounds for the initial higher-order Schippers-Schwarzian derivatives $σ_3(f)(0)$ and $σ_4(f)(0)$ for several subclasses of univalent and starlike functions in the unit disk. The functions in these classes are defined by subordination to domains bounded by an exponential-sine curve, a cardioid, or a petal-shaped curve. We determine the sharp bounds and find the corresponding extremal functions for each invariant in these subclasses. As an application, we also obtain sharp bounds for the initial Grunsky coefficients $ω_{1,1}$ and $ω_{1,2}$.
