有界非零函数的Landau问题

The Landau Problem for Univalent BoundedNonvanishing Functions

主要讨论了正则的有界非零函数f(z)=a0+a1z+…+anzn+…(a0≠0)在单位圆|z|<1内的上界问题,利用正则的有界非零函数的性质、极值原理和三角不等式,对正则的有界非零函数前五项系数和|a0+a1+a2+a3+a4|的上界进行估计,得到其上界一个新的表达式,从而推广了Krzyz猜测问题。

This paper is to discuss the problem of finding upper bound for univalent nonvanishing functions f（z）=a0＋a1z＋…＋anz^n＋…（a0≠0）in the unit disk｜z｜〈1.Regular use of univalent nonvanishing functions of the nature,the extreme value theory and the triangular inequality.The univalent nonvanishing functions of the first five coefficient ｜a0＋a1＋a2＋a3＋a4｜is estimated,to get a new expression of the upper bound,thereby promoting the issue of the Krzyz guess.