有界非零函数的Landau问题  

The landau problem for bounded nonvanishing functions

作　　者：苑文法[1] 王平安[1] 庞永峰[1] 

机构地区：[1]西安建筑科技大学理学院,陕西西安710055

出　　处：《西安建筑科技大学学报（自然科学版）》2006年第5期717-720,723,共5页Journal of Xi'an University of Architecture & Technology(Natural Science Edition)

基　　金：校基础研究基金项目(JC0621)

摘　　要：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四项系数的和a0+a1+a2+a3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.In this paper, the problem of above bound of regular bounded nonvanishing functions f（z）=a0＋a1z＋…＋anz^n＋…（a0≠0） Λ in the unit disk ｜z｜〈1 is put to diseussion. That is, we find sup ｜a0＋a1＋a2＋a3｜ for the sum of first four coefficients in expansion of f（x）. The properties of the bounded nonvanishing functions, the principle of the extremum and triangle inequality are put to use. And a new expression of above bound is obtained. The result helps generalize the problem of Krzyz＇s conjecture.

关 键 词：Landau问题 正则函数 非零函数 Krzyz猜测 

分 类 号：O174.30[理学—数学] C50[理学—基础数学]