单叶有界非零函数的系数问题

Coefficient Problem for Univalent Bounded Non-Vanishing Functions

文中讨论了正则单叶非零函数f(z)=a0+a1z+…anzn+…(a0≠0)在单位圆|z|<1内的系数估计问题,当n=2和n=3时,运用极值原理和有界正则函数的性质对|a0+a1+a2|和|a0+a1+a2+a3|的上界进行估计,得到其上界的估计式,进而推广了Krzyz猜测。

This paper studied the estimation problem of the coefficients for the univalent bounded non-vanishing functions f（z） =a0 ＋ a1z ＋ …anzn ＋ … （a0 ≠ 0） in the unit circle ｜ z ｜ 〈 1.When n =2 and n =3,this paper,uses the maximum principle and the properties of the bounded regular function,estimates the upper bound of ｜ a0 ＋ a1 ＋ a2 ｜ and ｜ a0 ＋a1 ＋ a2 ＋ a3 ｜,and obtains their upper bound estimator.This method can be extended to the Krzyz conjecture. Keywords：univalent bounded non-vanishing functions; Landau problem; Krzyz conjecture