| Approximation of Nearest Common Fixed Point of Nonexpansive Mappings in Hilbert Spaces |
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| 引用本文： | Shi Sheng ZHANG H.W. JOSEPH LEE Chi Kin CHAN. Approximation of Nearest Common Fixed Point of Nonexpansive Mappings in Hilbert Spaces[J]. 数学学报(英文版), 2007, 23(10): 1889-1896. DOI: 10.1007/s10114-005-0821-0 |
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| 作者姓名： | Shi Sheng ZHANG H.W. JOSEPH LEE Chi Kin CHAN |
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| 作者单位： | [1]Department of Mathematics, Yibin University, Yibin 644007, P. R. China [2]Department of Mathematics, Sichuan University, Chengdu 610064, P. R. China [3]Department of Applied Mathematics, The Hong Kong Polytechnic University, Hung Horn, Kowloon, Hong Kong, P. R. China |
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| 基金项目： | Supported by The Research Foundation Grant of The Hong Kong Polytechnic University and Yibin University （2005Z3） |
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| 摘 要： | The purpose of this paper is to study the convergence problem of the iteration scheme xn＋l = λn＋1y ＋ （1 - λn＋1）Tn＋1xn for a family of infinitely many nonexpansive mappings T1, T2,... 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 some recent results.
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| 关 键 词： | 共同固定点 逼近 非扩张映射 迭代 |
| 收稿时间： | 2005-06-06 |
| 修稿时间： | 2005-06-06 |
Approximation of Nearest Common Fixed Point of NonexpansiveMappings in Hilbert Spaces |
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| Shi Sheng Zhang,H. W. Joseph Lee,Chi Kin Chan. Approximation of Nearest Common Fixed Point of NonexpansiveMappings in Hilbert Spaces[J]. Acta Mathematica Sinica(English Series), 2007, 23(10): 1889-1896. DOI: 10.1007/s10114-005-0821-0 |
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| Authors: | Shi Sheng Zhang H. W. Joseph Lee Chi Kin Chan |
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| Affiliation: | (1) Department of Mathematics, Yibin University, Yibin 644007, P. R. China;(2) Department of Mathematics, Sichuan University, Chengdu 610064, P. R. China;(3) Department of Applied Mathematics, The Hong Kong Polytechnic University, Hung Hom, Kowloon, 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 some recent results. Supported by The Research Foundation Grant of The Hong Kong Polytechnic University and Yibin University (2005Z3) |
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| Keywords: | common fixed point family of nonexpansive mappings nearest point projection iterative scheme |
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