| Hilbert空间中非扩张映象的最近的公共不动点的逼近问题 |
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| 引用本文： | 张石生,李向荣,陈志坚.Hilbert空间中非扩张映象的最近的公共不动点的逼近问题[J].数学学报,2006,49(6):1297-130. |
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| 作者姓名： | 张石生 李向荣 陈志坚 |
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| 作者单位： | [1]宜宾学院数学系,宜宾644007 [2]香港理工大学应用数学系,香港 |
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| 摘 要： | 本文在Hilbert空间的框架下,研究无限族非扩张映象T_1,T_2,…的迭代程序x_n+1=λ_(n+1)y+(1-λ_(n+1))T_(n+1)x_n的收敛性问题．在适当的条件下,证明了该迭代序列收敛于这一非扩张映象族的最近的公共不动点．其结果改进和推广了引文中相应的结果．
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| 关 键 词： | 公共不动点 非扩张映象 最近点投影 |
| 文章编号： | 0583-1431（2006）06-1297-06 |
| 收稿时间： | 2005-02-06 |
| 修稿时间： | 2005-02-062005-09-15 |
On the Problem of Nearest Common Fixed Point of Nonexpansive Mappings |
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| Shi Sheng ZHANG,Joseph LEE,Chi Kin CHEN.On the Problem of Nearest Common Fixed Point of Nonexpansive Mappings[J].Acta Mathematica Sinica,2006,49(6):1297-130. |
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| Authors: | Shi Sheng ZHANG Joseph LEE Chi Kin CHEN |
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| Institution: | Department of Mathematics, Yibin University, Yibin 644007, P. R. China Department of Applied Mathematics, The Hong Kong Polytechnic University, Hong Kong, P, R. China |
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| Abstract: | The purpose of this paper is to study the convergence problem of the iteration scheme x_(n+1)=λ_n+1y+(1-λ_n+1)T_(n+1)x_n for a family of infinitely many nonexpansive mappings T_1,T_2,...in a Hilbert space.It is proved that under suitable conditions this iteration scheme converges strongly to the nearest common fixed point of this family of nonexpansive mappings.The results presented in this paper extend and improve the corresponding results. |
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| Keywords: | common fixed point the family of nonexpansive mappings nearest pointprojection |
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