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Title

On the stability of solutions for the generalized vector quasi-equilibrium problems via free-disposal set.

Authors

Wang, Jingjing; Peng, Zaiyun; Lin, Zhi; Zhou, Daqiong

Abstract

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 (△), 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.

Subjects

QUASI-equilibrium; VECTOR spaces

Publication

Journal of Industrial & Management Optimization, 2021, Vol 17, Issue 2, p869

ISSN

1547-5816

Publication type

Academic Journal

DOI

10.3934/jimo.2020002

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