| 有界非零函数的Landau问题 |
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| 引用本文： | 苑文法,段晓婧,张敏. 有界非零函数的Landau问题[J]. 延安大学学报(自然科学版), 2010, 29(4): 18-21 |
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| 作者姓名： | 苑文法 段晓婧 张敏 |
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| 作者单位： | 西安建筑科技大学数学系,陕西西安710055 |
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| 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。
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| 关 键 词： | Landau问题 正则函数 非零函数 Krzyz猜测 |
The Landau Problem for Univalent BoundedNonvanishing Functions |
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| YUAN Wen-fa,DUAN Xiao-jing,ZHANG MIN. The Landau Problem for Univalent BoundedNonvanishing Functions[J]. Journal of Yan'an University(Natural Science Edition), 2010, 29(4): 18-21 |
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| Authors: | YUAN Wen-fa DUAN Xiao-jing ZHANG MIN |
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| Affiliation: | (Department of Mathematics,Xian University of Architecture and Technology,Xian 710055,China) |
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| Abstract: | 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. |
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| Keywords: | Landau problem univalent functions nonvanishing functions Krzyz guess |
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