| 非扩张映像不动点新的简单逼近算法 |
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| 引用本文： | 苏永福.非扩张映像不动点新的简单逼近算法[J].系统科学与数学,2010,30(5):659-664. |
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| 作者姓名： | 苏永福 |
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| 作者单位： | 天津工业大学理学院数学系,天津,300160 |
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| 摘 要： | 提出了一个简单的非扩张映像不动点的逼近算法,该算法通过非迭代的逼近序列来实现.从算法的复杂性来看,提出的算法比经典的Mann迭代算法、Ishikawa迭代算法和Halpern迭代算法更简单.提出的算法紧密联系着非扩张映像不动点的存在性,因此,还得到了非扩张映像的新不动点定理, 拓展和改进了经典的Goebel-Kirk,Kim-Xu等作者的结果.
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| 关 键 词： | 非扩张映像 逼近算法 不动点 弱收敛. |
| 收稿时间： | 2008-8-25 |
| 修稿时间： | 2010-4-21 |
NEW SIMPLE APPROXIMATION ALGORITHM OF FIXED POINT FOR NONEXPANSIVE MAPPINGS |
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| SU Yongfu.NEW SIMPLE APPROXIMATION ALGORITHM OF FIXED POINT FOR NONEXPANSIVE MAPPINGS[J].Journal of Systems Science and Mathematical Sciences,2010,30(5):659-664. |
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| Authors: | SU Yongfu |
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| Institution: | Department of Mathematics, School of Science, Tianjin Polytechnic University Tianjin, Tianjin 300160 |
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| Abstract: | The purpose of this article is to establish new simple approximative algorithms of fixed point for nonexpansive mappings and to prove new fixed point theorems for nonexpansive mappings in the reflexive Banach spaces. The approximate algorithms presented in this article are simpler than Mann, Ishikawa and Halpern iterative algorithms. The weak and strong convergence theorems are proved respectively. The new fixed point theorems presented here improve and extend the related results of Goebel-Kirk, Kim-Xu and others in some respects. |
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| Keywords: | Nonexpansive mappings approximation algorithm fixed point weak convergence strong convergence |
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