Banach空间中Noor型变分不等式的广义投影法

数学物理学报 ›› 2010, Vol. 30 ›› Issue (3): 808-817.

Banach空间中Noor型变分不等式的广义投影法

徐永春¹, 何欣枫², 侯志彬², 何震^2**

1. 河北北方学院数学系河北张家口 075000|2. 河北大学数学与计算机学院河北保定 |071002

收稿日期:2008-12-11 修回日期:2009-10-08 出版日期:2010-05-25 发布日期:2010-05-25
基金资助:
教育部重点课题项目(207104)、国家自然科学基金项目(60873203)和张家口市科学技术研究与发展计划项目(0811024B-5)资助

Generalized Projection Methods for Noor Variational Inequalities in Banach Spaces

XU Yong-Chun¹, HE Xin-Feng², HOU Zhi-Bin², HE Zhen^2**

1. Department of Mathematics, Hebei North College, Hebei Zhangjiakou 075000|
2. College of Mathematics and Computer, Hebei University, Hebei Baoding 071002

Received:2008-12-11 Revised:2009-10-08 Online:2010-05-25 Published:2010-05-25
Supported by:
教育部重点课题项目(207104)、国家自然科学基金项目(60873203)和张家口市科学技术研究与发展计划项目(0811024B-5)资助

摘要/Abstract

摘要：

该文提出并分析了用广义投影方法解Noor型广义变分不等式问题. 在较弱的条件下考虑了一个迭代格式的收敛性. 由于广义变分不等式包含了许多变分不等式和相补问题为特例, 因此该文得出的结果可以应用到这些问题中. 这些结果是以前众多学者所做工作的完善和改进.

关键词: 广义投影映射, Noor型广义变分不等式, 一致光滑Banach空间, 李雅普诺夫泛函

Abstract:

In this paper, we suggest and analyze generalized projection methods for finding the elements of the set of solutions of the generalized variational inequalities. We also consider the convergence analysis of the suggested iterative schemes under some mild conditions. Since the generalized variational inequalities include variational inequalities and complementarity problems as special cases, results obtained in this paper continue to hold for these problems. Results obtained in this paper may be viewed as an refinement and improvement of the previously known results.

Key words: Generalized projection mapping, Generalized variational inequalities, Uniformly smooth Banach space, Lyapunov functional

中图分类号:

47H05

徐永春, 何欣枫, 侯志彬, 何震. Banach空间中Noor型变分不等式的广义投影法[J]. 数学物理学报, 2010, 30(3): 808-817.

XU Yong-Chun, HE Xin-Feng, HOU Zhi-Bin, HE Zhen. Generalized Projection Methods for Noor Variational Inequalities in Banach Spaces[J]. Acta mathematica scientia,Series A, 2010, 30(3): 808-817.

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