数学物理学报 ›› 2009, Vol. 29 ›› Issue (3): 823-831.

• 论文 • 上一篇    

带误差的合成隐迭代新算法

  

  1. (宜宾学院数学系 |四川 宜宾 644007)
  • 收稿日期:2007-11-19 修回日期:2008-12-10 出版日期:2009-06-25 发布日期:2009-06-25
  • 基金资助:

    四川省教育厅青年项目(08ZB002)和四川省教育厅自然科学基金(08ZC001)资助

New Composite Implicit Iterative Scheme With Errors

  1. (Department of Mathematics,   |Yibin University, Sichuan Yibin 644000)
  • Received:2007-11-19 Revised:2008-12-10 Online:2009-06-25 Published:2009-06-25
  • Supported by:

    四川省教育厅青年项目(08ZB002)和四川省教育厅自然科学基金(08ZC001)资助

摘要:

该文参照Banach压缩映象原理 合理地引进了一涉及有限族渐进非扩张映象的具误差的合成隐迭代式. 在适当条件下 证得了该迭代序列给出的序列弱收敛与强收敛到有限族 渐进非扩张映象的一公共不动点, 并 由此得出该合成隐迭代式导出的一非隐迭代算法的弱收敛 与强收敛的新定理. 值得一提的是, 这是在未增加任何附加条件的情况下 将2006年一文献的主要结果由隐迭代算法改进为非隐的显式迭代算法.

关键词: 一致凸性, 渐进非扩张映象, 公共不动点

Abstract:

In this paper, a new composite implicit iterative process with errors for a family of asymptotically nonexpansive mappings was reasonably introduced in view of Banach's contraction principle,  and a new theorem  for weak and strong convergence  was obtained under some suitable conditions,  which deduced a new convergent theorem for a non-implicit iterative process with errors. It is worthy to say that  this result extend the corresponding results of  S.S.Chang [1] from implicit iterative process to non-implicit algorithm without any additive assumptions.

Key words: Uniform , convexity, Asymptotically nonexpensive mappings, Common fixed point

中图分类号: 

  • 47H09