Hilbert空间中非扩张余弦族的显式、隐式和黏性迭代

摘要/Abstract

摘要：

研究了Hilbert空间中一些逼近单参数非扩张余弦族公共不动点的迭代格式. 借助余弦族理论, 在较弱的条件下分别对显式、隐式和黏性的迭代过程建立了一系列的收敛定理. 结果表明上述三种迭代过程适用于非扩张余弦族; 并且隐式和黏性迭代格式在收敛性上优越于显式迭代格式.

关键词: 非扩张余弦族, 公共不动点, 显式迭代格式, 隐式迭代格式, 黏性迭代格式

Abstract:

In this paper some iterative schemes to approximate a common fixed point of one-parameter nonexpansive cosine family are investigated in Hilbert spaces. By using the theory of cosine families, a series of new convergence theorems are established under some mild conditions for the explicit, implicit and viscosity iteration processes, respectively. Our results show that the above three iterative methods are applicable to the nonexpansive cosine families; and the implicit and viscosity iterations are superior the explicit iteration in convergence.

Key words: Nonexpansive cosine family, Common fixed point, Explicit iteration process, Implicit iteration process, Viscosity iteration process

中图分类号:

47H09

肖建中, 严洁, 朱杏华. Hilbert空间中非扩张余弦族的显式、隐式和黏性迭代[J]. 数学物理学报, 2014, 34(6): 1518-1531.

XIAO Jian-Zhong, YAN Jie, ZHU Xing-Hua. Explicit, Implicit and Viscosity Iterations for Nonexpansive Cosine Families in Hilbert Spaces[J]. Acta mathematica scientia,Series A, 2014, 34(6): 1518-1531.

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