| Browder-Petryshyn 型的严格伪压缩映射的粘滞迭代逼近方法 |
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| 引用本文： | 陈汝栋,宋义生. Browder-Petryshyn 型的严格伪压缩映射的粘滞迭代逼近方法[J]. 系统科学与数学, 2006, 26(6): 651-657 |
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| 作者姓名： | 陈汝栋 宋义生 |
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| 作者单位： | 天津工业大学数学研究所、数学系,天津,300160 |
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| 基金项目： | 国家自然科学基金资助课题(10471003,10271001)． |
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| 摘 要： | 主要研究Browder-Petryshyn型的严格伪压缩映射的粘滞迭代逼近过程,证明了Browder-Petryshyn型的严格伪压缩映射的不动点集F(T)是闭凸集．在q-一致光滑且一致凸的Banach空间中,对于严格伪压缩映射T,利用徐洪坤在2004年引进的粘滞迭代得到的序列弱收敛于T的某个不动点．同时证明了Hilbert空间中Browder-Petryshyn型的严格伪压缩映射的相应迭代序列强收敛到T的某个不动点,其结果推广与改进了徐洪坤2004年的相应结果．
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| 关 键 词： | 严格伪压缩映射 粘滞迭代方法 不动点 闭凸集 |
| 收稿时间： | 2005-02-04 |
| 修稿时间： | 2005-02-04 |
Viscosity approximation methods for strictly pseudocontractive mappings of Browder-petryshyn type |
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| Chen Rudong,Song Yisheng. Viscosity approximation methods for strictly pseudocontractive mappings of Browder-petryshyn type[J]. Journal of Systems Science and Mathematical Sciences, 2006, 26(6): 651-657 |
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| Authors: | Chen Rudong Song Yisheng |
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| Affiliation: | Department of Mathematics, Tianjin Polytechnic University, Tianjin 300160 |
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| Abstract: | In this paper, we study viscosity approximation process for strictly pseudo-contractive mapping T of Browder-Petryshyn type and prove that the fixed point set F(T) is a closed convex subset. We obtain a weak convergence theorem of strictly pseudocontractive self-mapping T of a closed convex subset K of a q-uniformly smooth Banach space which is also uniformly convex using viscosity approximation process {xt}, where xt = tf(xt) (1-t)Txt, f is an L-Lipschitz strongly pseudocontractive maping. We also prove that {xt} strongly converge to a fixed point of T which solves some variational inequality in Hilbert space. The results extend and improve the corresponding results of Xu Hongkun(2004). |
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| Keywords: | Strictly pseudocontractive mapping viscosity approximation fixed points closed convex set. |
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