Banach空间中一类变分不等式的强收敛定理

刘英;佟慧

系统科学与数学 ›› 2010, Vol. 30 ›› Issue (4) : 468-475.

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系统科学与数学 ›› 2010, Vol. 30 ›› Issue (4) : 468-475. DOI: 10.12341/jssms08962
论文

Banach空间中一类变分不等式的强收敛定理

    刘英,佟慧
作者信息 +

Strong Convergence Theorems for Variational Inequalities in a Banach Space

    LIU Ying, TONG Hui
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摘要

应用广义投影算子引入了一类新的CQ迭代方法,并用此方法在Banach空间的非紧子集上证明了一个关于变分不等式的强收敛定理;这一定理所用的迭代方法不同于最近的一些相关定理,而且所得结论更加具体;最后,又用这一结果,考虑了在Banach空间,算子T的零点问题.

Abstract

In this paper, a new CQ iterative method is introduced by using the generalized projection operator, and then a strong convergence theorem for variational inequality in noncompact subset of Banach space is proved by the method. This theorem is more concrete than previous related results. Finally, the problem of zero point for an operator in Banach space is investigated by the resultant theorem.

关键词

变分不等式 / CQ迭代法 / 广义投影算子 / 紧算子.

Key words

Variational inequality / CQ iterative method / generalized projection operator / compact operator.

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刘英 , 佟慧. Banach空间中一类变分不等式的强收敛定理. 系统科学与数学, 2010, 30(4): 468-475. https://doi.org/10.12341/jssms08962
LIU Ying , TONG Hui. Strong Convergence Theorems for Variational Inequalities in a Banach Space. Journal of Systems Science and Mathematical Sciences, 2010, 30(4): 468-475 https://doi.org/10.12341/jssms08962
中图分类号： 47H09    47H05   
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