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| 正则函数的修正的Cauchy型积分算子的不动点定理及迭代构造 | |
| 引用本文： | 王丽萍,彭维玲,肖卓峰. 正则函数的修正的Cauchy型积分算子的不动点定理及迭代构造[J]. 数学研究及应用, 2008, 28(3): 589-604. DOI: 10.3770/j.issn.1000-341X.2008.03.019 |
| 作者姓名： | 王丽萍 彭维玲 肖卓峰 |
| 作者单位： | 河北师范大学数学与信息科学学院, 河北 石家庄 050016;通化师范学院数学系, 吉林 通化 134002;河北师范大学附属民族师范学院, 河北 石家庄 050091 |
| 基金项目： | 国家自然科学基金(No.10771049; 10771050); 河北省自然科学基金(No.A2007000225); 河北师范大学基金(No.L2007Q05); 河北省教育科学研究``十一五'规划课题(No.O8020147). |
| 摘 要： | 本文第一部分讨论了正则函数的{small Cauchy}型积分算子$T[f]$的{small H"{o}lder}连续性及此积分算子$T[f]$的范数与$f$的范数之间的关系.第二部分引入了修正的Cauchy型积分算子$small widetilde{T}$,首先利用压缩映射原理证明了$small widetilde{T}$算子具有不动点,然后给出了其不动点的迭代序列并证明了此序列强收敛于$small widetilde{T}$算子的不动点. |
| 关 键 词： | Clifford分析 正则函数 Cauchy型积分 不动点 Mann迭代. |
| 收稿时间： | 2007-07-23 |
| 修稿时间： | 2008-04-16 |
The Fixed Point Theorem and the Iterative Approximation of Modified Cauchy Integral Operator of Regular Functions |
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| WANG Li Ping,PENG Wei Ling and XIAO Zhuo Feng. The Fixed Point Theorem and the Iterative Approximation of Modified Cauchy Integral Operator of Regular Functions[J]. Journal of Mathematical Research with Applications, 2008, 28(3): 589-604. DOI: 10.3770/j.issn.1000-341X.2008.03.019 | |
| Authors: | WANG Li Ping PENG Wei Ling XIAO Zhuo Feng |
| Affiliation: | 1. School of Mathematics and Information Science, Hebei Normal University, Hebei 050016, China 2. Department of Mathematics, Tonghua Teachers College, Jilin 134002, China 3. Tibetan College of Hebei Normal University, Hebei 050091, China |
| Abstract: | In the first part of this paper, we discuss the H"{o}lder continuity of the cauchy integral operator for regular functions and the relation between $|T[f]|_{alpha}$ and $|f|_{alpha}$. In the second part of this paper, we introduce the modified cauchy integral operator $widetilde{T}$ for regular functions. Firstly, we prove that the operator $widetilde{T}$ has a unique fixed point by the Banach's Contraction Mapping Principle. Secondly, we give the Mann iterative sequence, and then we show the iterative sequence strongly converges to the fixed point of the operator $widetilde{T}$. |
| Keywords: | real Clifford analysis regular function cauchy integral the fixed point mann iteration. |
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