数学物理学报 ›› 2014, Vol. 34 ›› Issue (1): 1-8.

• 论文 •    下一篇

Banach空间中关于非扩张映射的修改的Mann 迭代算法的强收敛定理

蔡钢|步尚全   

  1. 清华大学数学科学系 |北京 100084
  • 收稿日期:2012-05-17 修回日期:2013-08-21 出版日期:2014-02-25 发布日期:2014-02-25
  • 基金资助:

    国家自然科学基金资助项目(11171172) 和高等学校博士学科点专项科研基金(20120002110044)资助.

Strong Convergence Theorems of a Modified Mann Iterative Method for Nonexpansive Mappings in Banach Spaces

 CAI Gang, BU Shang-Quan   

  1. Department of Mathematical Sciences, Tsinghua University, Beijing 100084
  • Received:2012-05-17 Revised:2013-08-21 Online:2014-02-25 Published:2014-02-25
  • Supported by:

    国家自然科学基金资助项目(11171172) 和高等学校博士学科点专项科研基金(20120002110044)资助.

摘要:

该文在Banach 空间里引进一种新的修改的Mann 算法, 来寻求一族无限个非扩张映射的公共元素. 在适当条件下, 得到了一个强收敛定理. 所得结果改进和推广了许多最近的相关结果.

关键词: 强收敛, 不动点, 非扩张映射, Banach 空间

Abstract:

In this paper, we introduce a new modified Mann iterative algorithm for finding a common element of the set of common fixed points of infinite family of nonexpansive mappings in a real Banach space. Then we prove a strong convergence theorem under some suitable conditions. Our results improve and extend the corresponding results announced by many others in the literature.

Key words: Strong convergence, Fixed point,  Nonexpansive mapping, Banach space

中图分类号: 

  • 47H10