某类多叶解析函数的性质

设A(p)(p是指数，p≥1）表示在单位圆盘E内形如f(z)=z^p ap 1z^p 1…的解析函数族。本文引进了新的函数子类Hσ（p,α），找出了Hσ（p,α）闭凸包的极值点并给出精确的系数估计，还讨论了Hσ（p,α）其它一些有趣的性质。

Properties of Certain Multivalent Analytic Functions

Let A(p) (p is an integer, p ≥ 1) be the class of functions f(z) = zp + ap+1zp+1 +… which are analytic in the unit disk E. In this paper a new subclass Hσ(p,α) of A(p) is introduced.We find the extreme point of closed convex hull of the class Hσ(p, α) and then determine the sharp coefficient bounds. Some other interesting properties of the class Hσ (p, α) are also investigated.