单叶函数若干子类的Hankel行列式H2（3）

Hankel Determinants H2（3） for Some Subclasses of Univalent Functions

对α阶星象函数S^*(α)、α阶凸函数K(α)和导数的实部大于α的函数类R(α)的二阶Hankel行列式H2(3)分别进行研究.利用已知的正实部函数类的系数估计来估计出给定的3个函数类的H2(3)模的上界.其中,R(α)对应H2(3)模的上界是最佳的.当系数a2=0时,得到S^*(α)和K(α)对应H2(3)模的最佳上界.

The second Hankel determinant H2(3)for the classes S^*(α)of starlike functions of orderα,K(α)of convex functions of orderαand R(α)of functions whose real part of derivative is greaterthanαare studied,respectively.By using the coefficient estimates of the known function class with positive real part,the up-per bounds of modules on H2(3)of three given function classes are estimated.The upper bound of module on H2(3)for R(α)is sharp.Furthermore,we get the sharp bounds on H2(3)for S^*(α)and K(α)when the coe fficient a2=0.