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On the stability of solutions for the generalized vector quasi-equilibrium problems via free-disposal set
Journal of Industrial and Management Optimization ( IF 1.3 ) Pub Date : 2020-01-08 , DOI: 10.3934/jimo.2020002
Jingjing Wang , , Zaiyun Peng , Zhi Lin , Daqiong Zhou

In this paper, we mainly discuss the stability of generalized vector quasi-equilibrium problems (GVQEPs) where the ordering relations are defined by free-disposal set. Firstly, by virtue of the oriented distance function $ (\triangle) $, gap functions for (GVQEPs) are given and some properties of them are studied. Then, under some types of continuity assumption, the sufficient conditions of the upper semicontinuity and the upper Painlevé-Kuratowski convergence of solutions for (GVQEPs) are talked about. Moreover, sufficient and necessary conditions of the lower semicontinuity and the lower Painlevé-Kuratowski convergence of solutions for (GVQEPs) are obtained in normed linear spaces. Some examples are given to illustrate the results, and our results are new and extend some known results in the literature.

中文翻译:

自由处置集的广义矢量拟平衡问题解的稳定性

在本文中,我们主要讨论广义矢量拟均衡问题(GVQEP)的稳定性,其中有序关系由自由处理集定义。首先,利用定向距离函数$(\ triangle)$,给出了(GVQEPs)的间隙函数,并研究了它们的一些性质。然后,在某些类型的连续性假设下,讨论了(GVQEPs)的上半连续性和上Painlevé-Kuratowski收敛解的充分条件。此外,在赋范线性空间中获得了(GVQEP)解的较低半连续性和较低Painlevé-Kuratowski收敛的充分必要条件。给出了一些例子来说明结果,我们的结果是新的并且扩展了文献中的一些已知结果。
更新日期:2020-01-08
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