Stability for Parametric Vector Quasi-Equilibrium Problems With Variable Cones

Abstract

This article is devoted to the study of stability conditions for a class of quasi-equilibrium problems with variable cones in normed spaces. We introduce concepts of upper and lower semicontinuity of vector-valued mappings involving variable cones and their properties, we also propose a key hypothesis. Employing this hypothesis and such concepts, we investigate sufficient/necessary conditions of the Hausdorff semicontinuity/continuity for solution mappings to such problems. We also discuss characterizations for the hypothesis which do not contain information regarding solution sets. As an application, we consider the special case of traffic network problems. Our results are new or improve the existing ones.

Keywords:

• Hausdorff semicontinuity
• quasi-equilibrium problem
• stability
• traffic network problem

AMS CLASSIFICATION:

• 49K40
• 90C31
• 91B50

Acknowledgments

The authors thank the editor and three referees for their valuable remarks and suggestions that helped them significantly improve the article.

Additional information

Funding

This research is funded by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under Grant Number 101.01-2017.18.