| 修正的isotonic算子的不动点与Mann迭代 |
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| 引用本文： | 王丽萍,许作良.修正的isotonic算子的不动点与Mann迭代[J].数学研究及应用,2013,33(5):587-597. |
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| 作者姓名： | 王丽萍 许作良 |
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| 作者单位： | 中国人民大学信息学院, 北京 100872; 河北师范大学数学与信息科学学院, 河北 石家庄 050016;中国人民大学信息学院, 北京 100872 |
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| 基金项目： | 国家自然科学基金(Grant Nos.10771049; 11171349),河北省自然科学基金 (Grant No.A2010000346). |
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| 摘 要： | 在论文的第一部分, 研究与讨论了isotonic函数的Cauchy型奇异积分算子$T$的 H\"{o}lder连续性及$\|Tf]\|_{\alpha}$与$\|f\|_{\alpha}$间的关系. 在第二部分, 引入了isotonic函数的修正的Cauchy型奇异积分算子$T'$, 首先利用压缩不动点定理证明此修正的Cauchy型奇异积分算子$T'$存在唯一不动点, 然后给出其不动点的Mann迭代序列并证明此序列强收敛于$T'$算子的不动点.
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| 关 键 词： | Clifford分析 isotonic算子 不动点定理 Mann迭代序列. |
| 收稿时间： | 2012/7/30 0:00:00 |
| 修稿时间： | 6/4/2013 12:00:00 AM |
The Fixed Point and Mann Iteration of a Modified Isotonic Operator |
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| Liping WANG and Zuoliang XU.The Fixed Point and Mann Iteration of a Modified Isotonic Operator[J].Journal of Mathematical Research with Applications,2013,33(5):587-597. |
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| Authors: | Liping WANG and Zuoliang XU |
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| Institution: | School of Information, Renmin University of China, Beijing 100872, P. R. China; College of Mathematics and Information Science, Hebei Normal University, Hebei 050024, P. R. China;School of Information, Renmin University of China, Beijing 100872, P. R. China; |
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| Abstract: | This paper consists of two parts. In the first part, we discuss the H\"{o}lder continuity of Cauchy-type integral operator $T$ of isotonic functions and the relationship between $\|Tf]\|_{\alpha}$ and $\|f\|_{\alpha}$. In the second part, firstly, we introduce a modified Cauchy-type integral operator $T'$ and demonstrate that the operator $T'$ has a unique fixed point by the Contraction Mapping Principle. Then we give the Mann iterative sequence and prove that the Mann iterative sequence strongly converges to the fixed point of the modified Cauchy-type integral operator $T'$. |
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| Keywords: | Clifford analysis isotonic operator the fixed point theorem Mann iteration |
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