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

Jingjing Wang; Zaiyun Peng; Zhi Lin; Daqiong Zhou

doi:10.3934/jimo.2020002

Article Contents

2021, Volume 17, Issue 2: 869-887. Doi: 10.3934/jimo.2020002

This issue Previous Article Optimal stop-loss reinsurance with joint utility constraints Next Article On correlated defaults and incomplete information

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

College of Mathematics and Statistics, Chongqing JiaoTong University, Chongqing 400074, China

^* Corresponding author: Zaiyun Peng
^* Corresponding author: Zaiyun Peng

Received: June 2018

Revised: March 2019

Early access: January 2020

Published: March 2021

The first and the fourth authors are supported by the Graduate Innovation Foundation of Chongqing Jiaotong University (2019S0123). The second author is supported by the National Natural Science Foundation of China (11301571), the Basic and Advanced Research Project of Chongqing (cstc2018jcyjAX0337), the Program for University Innovation Team of Chongqing (CXTDX201601022), the Innovation Project for Returned Overseas Scholars in Chongqing (cx2019148), the open project funded by the Chongqing Key Lab on ORSE (CSSXKFKTZ201801) and the Education Committee Project Foundation of Bayu Scholar. The third author is supported by the National Natural Science Foundation of China (11271389).

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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 $ (\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.

Keywords:

Generalized vector quasi-equilibrium problems,
free-disposal set,
the oriented distance function,
semicontinuity,
Painlevé-Kuratowski convergence.

Mathematics Subject Classification: 49K40, 90C31, 91B50.

Citation:

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Figure 1. the improvement set 1

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Figure 2. the improvement set 2

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Figure 3. the improvement set 3

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