一类隐式集值向量均衡问题解的存在性和解集的稳定性

李秋英;王三华

系统科学与数学 ›› 2011, Vol. 31 ›› Issue (1) : 1-012.

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系统科学与数学 ›› 2011, Vol. 31 ›› Issue (1) : 1-012. DOI: 10.12341/jssms09437
论文

一类隐式集值向量均衡问题解的存在性和解集的稳定性

    李秋英(1), 王三华(2)
作者信息 +

Existence and Stability for a Class of Implicit Set-Valued Vector Equilibrium Problems

    LI Qiuying(1), WANG Sanhua(2)
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摘要

研究一类隐式集值向量均衡问题,它是隐式向量均衡问题、隐式变分不等式问题、隐式相补问题、向量均衡问题和向量变分不等式问题等的推广.利用截口定理, 在 Hausdorff 拓扑线性空间的非紧子集上得出了一些隐式集值向量均衡问题解的存在性结果.并且还讨论了该隐式集值向量均衡问题解集的通有稳定性.这些结果推广和统一了近期的一些相关结果.

Abstract

In this paper, a class of implicit set-valued vector equilibrium problems is introduced and studied, which includes implicit vector equilibrium problems, implicit variational inequalities, implicit complementarity problems, vector equilibrium problems, vector variational inequalities as special cases. By using the section theorem, some existence results for implicit set-valued vector equilibrium problems
are obtained on a noncompact subset of a Haudorff topological vector space.
Furthermore, the stability of solution set for implicit set-valued vector equilibrium problems is discussed. These results extend and unify some recent results in the literature.

关键词

隐式集值向量均衡问题 / 存在性 / 稳定性 / 上半连续性 / 下半连续性.

Key words

Implicit set-valued vector equilibrium problem / existence / stability / upper semicontinuity / lower semicontinuity.

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李秋英 , 王三华. 一类隐式集值向量均衡问题解的存在性和解集的稳定性. 系统科学与数学, 2011, 31(1): 1-012. https://doi.org/10.12341/jssms09437
LI Qiuying , WANG Sanhua. Existence and Stability for a Class of Implicit Set-Valued Vector Equilibrium Problems. Journal of Systems Science and Mathematical Sciences, 2011, 31(1): 1-012 https://doi.org/10.12341/jssms09437
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