从属于指数函数的星像函数子类的四阶Hankel行列式

设$\mathcal{A} $表示单位圆盘D={z∈${\mathbb{C}} $ ∶ |z| < 1}内解析且具有如下形式 $f(z)=z+\sum\limits_{n=2}^{\infty} a_{n} z^{n}$ 的函数族. 文章研究了在单位圆盘D上与指数函数有关的解析函数类S_e*: $S_{e}^{*}=\left\{f \mid \frac{z f^{\prime}(z)}{f(z)} \prec \mathrm{e}^{z} \quad(f \in \mathcal{A}, z \in D)\right\}$ 的四阶Hankel行列式H₄(1), 得到其上界估计.

The Fourth-order Hankel Determinant for Certain Subclasses of Star-like Functions Subordinate to Exponential Function

Let $\mathcal{A} $ be a family of analytic functions with are the form $f(z)=z+\sum\limits_{n=2}^{\infty} a_{n} z^{n}$ on the open unit disk D. A class of analytic functions S_e* which are defined on the open unit cicle D and associated with exponential function is introduced, that is $S_{e}^{*}=\left\{f \mid \frac{z f^{\prime}(z)}{f(z)}\prec\mathrm{e}^{z} \quad(f \in \mathcal{A}, z \in D)\right\}.$ And the upper bound of the fourth-order Hankel determinant H₄(1) for this function class S_e* associated with exponential function is given.