关于非扩张映射的不动点问题的粘性迭代算法的强收敛定理

数学物理学报 ›› 2015, Vol. 35 ›› Issue (3): 487-502.

关于非扩张映射的不动点问题的粘性迭代算法的强收敛定理

蔡钢

重庆师范大学数学科学学院重庆市 401331

收稿日期:2014-03-17 修回日期:2014-12-17 出版日期:2015-06-25 发布日期:2015-06-25
作者简介:蔡钢, caigang-aaaa@163.com
基金资助:
国家自然科学基金(11171172, 11401063)、高等学校博士学科点专项科研基金(20120002110044)、重庆市自然科学基金(cstc2014jcyjA00016) 和重庆师范大学博士启动基金(14XLB002)资助

Strong Convergence Theorems by A Viscosity Iterative Method for Fixed Point Problems of Nonexpansive Mappings in Banach Spaces

Cai Gang

School of Mathematical Sciences, Chongqing Normal University, Chongqing 401331

Received:2014-03-17 Revised:2014-12-17 Online:2015-06-25 Published:2015-06-25

摘要/Abstract

摘要：

该文首先研究吸引非扩张映射的性质, 然后在一致光滑 Banach 空间里, 用这些性质研究两个非扩张映射的不动点问题的粘性迭代算法.作为应用, 在 Banach 空间或 Hilbert 空间里, 得到了关于变分不等式问题, 不动点问题和均衡问题的强收敛定理. 所得结果提高和推广了许多最近的相关结果.

关键词: 不动点, 变分不等式, 强收敛, 非扩张映射, Banach 空间

Abstract:

In this paper, we first study some properties of attracting nonexpansive mappings. Furthermore, we use these properties to investigate some viscosity iterative methods for fixed point problems of two nonexpansive mappings in uniformly smooth Banach space. As an application, we obtain some strong convergence theorems for variational inequality problems, fixed point problems and equilibrium problems in Banach spaces or Hilbert spaces. The results obtained in this paper improve and extend many recent ones announced by many others in this literature.

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

中图分类号:

O177.91

蔡钢. 关于非扩张映射的不动点问题的粘性迭代算法的强收敛定理[J]. 数学物理学报, 2015, 35(3): 487-502.

Cai Gang. Strong Convergence Theorems by A Viscosity Iterative Method for Fixed Point Problems of Nonexpansive Mappings in Banach Spaces[J]. Acta mathematica scientia,Series A, 2015, 35(3): 487-502.

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