唐玉超,朱传喜.关于有限族Lipschitz映射多步Ishikawa迭代算法的收敛性及其应用[J].数学研究及应用,2013,33(4):463~474
关于有限族Lipschitz映射多步Ishikawa迭代算法的收敛性及其应用
Convergence of a Multistep Ishikawa Iteration Algorithm for a Finite Family of Lipschitz Mappings and Its Applications
投稿时间:2012-03-24  最后修改时间:2012-11-22
DOI:10.3770/j.issn:2095-2651.2013.04.009
中文关键词:  凸可行性问题  公共不动点  Lipschitz映射.
英文关键词:convex feasibility problem  common fixed point problem  Lipschitz mappings.
基金项目:国家自然科学基金(Grant No.11201216), 江西省自然科学基金(Grant No.20114BAB201004), 江西省教育厅基金(Grant No.GJJ12141).
作者单位
唐玉超 南昌大学数学系, 江西 南昌 330031; 西安交通大学数学系, 陕西 西安 710049 
朱传喜 南昌大学数学系, 江西 南昌 330031 
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中文摘要:
      本文的目的是研究Lipschitz映射公共不动点问题.基于传统的Ishikawa迭代和Noor迭代方法,我们引入多步Ishikawa迭代算法,并且分别给出了该算法强收敛于有限族拟-Lipschitz映射和伪压缩映射公共不动点的充分必要条件.此外,我们证明了该算法强收敛到非扩张映射的公共不动点.作为应用,我们给出数值试验证实所得的结论.
英文摘要:
      The purpose of this paper is to investigate the problem of finding a common fixed point of Lipschitz mappings. We introduce a multistep Ishikawa iteration approximation method which is based upon the Ishikawa iteration method and the Noor iteration method, and we prove some necessary and sufficient conditions for the strong convergence of the iteration scheme to a common fixed point of a finite family of quasi-Lipschitz mappings and pseudocontractive mappings, respectively. In particular, we establish a strong convergence theorem of the sequence generated by the multistep Ishikawa scheme to a common fixed point of nonexpansive mappings. As applications, some numerical experiments of the multistep Ishikawa iteration algorithm are given to demonstrate the convergence results.
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