Banach空间中广义变分不等式迭代算法的强收敛性

doi:10.3969/j.cnki.jdxb.2017.04.003

吉首大学学报（自然科学版）

Banach空间中广义变分不等式迭代算法的强收敛性

曾艳，陈国平

（1.吉首大学数学与统计学院，湖南吉首 416000;2.吉首市第一中学，湖南吉首 416000）

出版日期:2017-07-25 发布日期:2017-08-01
通讯作者: 陈国平（1964—），男，湖南邵阳人，吉首大学数学与统计学院教授，博士，主要从事应用数学研究.
作者简介:曾艳（1978—），女，湖南益阳人，吉首大学数学与统计学院硕士研究生，主要从事应用数学研究
基金资助:
国家自然科学基金资助项目（11661037）;湖南省自然科学基金资助项目（2016JJ6122）

Strong Convergence of Iterative Algorithms for a Class of Generalized Variational Inequality Problems in Banach Spaces

ZENG Yan，CHEN Guoping

(1.College of Mathematics and Statistics，Jishou University，Jishou 416000，Hunan China;2.No.1 Middle School of Jishou City，Jishou 416000，Hunan China)

Online:2017-07-25 Published:2017-08-01

摘要/Abstract

摘要：

利用修改的外梯度方法，结合修改的Mann迭代方法，讨论了一类Banach空间中严格伪压缩映像的广义变分不等式问题.在适当的条件下，证明了算法所得到的序列强收敛到相应问题的解.

关键词： 外梯度方法, 广义变分不等式, 迭代方法, 强收敛

Abstract:

In this paper，we disscuss a class of generalized variational inequality problems involved in strictly pseudo-contractive mapping in Banach spaces by using some new algorithms which couple modified extra-gradient method with extended Mann iteration.It is proved that the sequences generated by the proposed iterative algorithms converge strongly to the solution of the generalized variational inequality problem.The results presented in this paper extend and improve some well-known results in the literature.

Key words: extra-gradient method, generalized variational inequality problems, iterative algorithm, strong convergence

曾艳，陈国平. Banach空间中广义变分不等式迭代算法的强收敛性[J]. 吉首大学学报（自然科学版）, DOI: 10.3969/j.cnki.jdxb.2017.04.003.

ZENG Yan，CHEN Guoping. Strong Convergence of Iterative Algorithms for a Class of Generalized Variational Inequality Problems in Banach Spaces[J]. Journal of Jishou University（Natural Sciences Edition), DOI: 10.3969/j.cnki.jdxb.2017.04.003.

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Banach空间中广义变分不等式迭代算法的强收敛性

Strong Convergence of Iterative Algorithms for a Class of Generalized Variational Inequality Problems in Banach Spaces

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