从属于指数函数的星像函数子类的四阶Hankel行列式

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

摘要: 设\mathcalA 表示单位圆盘D=z∈\mathbbC ∶ |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 \fracz f^\prime(z)f(z) \prec \mathrme^z \quad(f \in \mathcalA, z \in D)\right\ 的四阶Hankel行列式H₄(1), 得到其上界估计.

Abstract: Let \mathcalA 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 \fracz f^\prime(z)f(z)\prec\mathrme^z \quad(f \in \mathcalA, 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.