渐近非扩张映象不动点的黏性混杂子序列迭代算法收敛性
Viscosity Hybrid Subsequence Iterative Algorithm for the Fixed Points of Asymptotic Nonexpansive Mappings
DOI: 10.12677/PM.2012.24031, PDF, HTML, 下载: 3,580  浏览: 11,682  国家自然科学基金支持
作者: 孙玮玮*, 王元恒*：浙江师范大学数理与信息工程学院
关键词: 渐近非扩张映象；不动点；黏性混杂迭代；子序列；Asymptotic Nonexpansive Mapping; Fixed Point; Viscosity Hybrid Iterative; Subsequence Sequence
摘要: 在Hilbert空间中研究了渐近非扩张映象T的不动点的一种新型黏性混杂子序列迭代法算法，并利用该迭代算法特点在一定条件下证明了迭代序列强收敛于T的不动点。其结果改进和推广了一些相应的近代结果。
Abstract:  A new viscosity hybrid subsequence iterative method for the fixed points of asymptotic nonexpansive mappings is given and studied in Hilbert spaces. The strong convergent theorem for this kind of the iterative sequences is proved. The results in the present paper extend and improve some resent results of other authors.
文章引用：孙玮玮, 王元恒. 渐近非扩张映象不动点的黏性混杂子序列迭代算法收敛性[J]. 理论数学, 2012, 2(4): 202-206. http://dx.doi.org/10.12677/PM.2012.24031

参考文献

[1] W. R. Mann. Mean value methods in iteration. Proceedings of American Mathematical Society, 1953, 4: 506-501.
[2] S. Ishikawa. Fixed points by a new iteration method. Proceedings of American Mathematical Society, 1974, 44: 147-150.
[3] B. Halpern. Fixed points of nonexpanding maps. Bulletin of the American Mathematical Society, 1967, 73: 957-961.
[4] H. K. Xu. Viscosity approximation methods for nonexpansive mappings. Journal of Mathematical Analysis and Applications, 2004, 298: 279-291.
[5] 张石生. Banach空间中非扩张映像的黏性逼近方法[J]. 数学学报(中文版), 2007, 50(3): 485-492.
[6] K. Nakajo, W. Takahash. Strong convergence theorems for nonexpansive mappings and nonexpansive semigroups. Journal of Mathematical Analysis and Applications, 2003, 279(2): 372-379.
[7] K. Nakajo, K. Shimoji and W. Takahashi. Strong convergence theorems by the hybrid method for families of nonexpansive mappings in Hilbert spaces. Taiwanese Journal of Mathematics, 2006, 10(2): 339-360.
[8] 黄建锋, 王元恒. 关于一种严格伪压缩映象Mann迭代序列的强收敛性[J]. 浙江师范大学学报(自然科学版), 2006, 29(4): 378-381.
[9] 刘立红, 陈东青. Hilbert空间k-严格伪压缩映像不动点的迭代算法[J]. 数学的实践与认识, 2010, 41(9): 11-17.
[10] 谈斌. 几类非线性算子零点或不动点迭代算法追究[D]. 军械工程学院, 2004: 6-11.
[11] 王元恒, 曾六川. Banach空间中广义投影变形迭代法的收敛性[J]. 数学年刊, 2009, 30A(1): 55-62.

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