On the stability of approximate solutions to set-valued equilibrium problems

Abstract

In this paper, we consider set-valued equilibrium problems in Hausdorff locally convex topological vector spaces. Based on linear scalarization techniques for sets, we study sufficient conditions for the stability of approximate solutions to such problems. Variational inequalities with equilibrium constraints and weak traffic network equilibrium problems are also discussed as applications of the main results.

Keywords:

• Equilibrium problem
• variational inequality
• linear scalarization
• stability of approximate solutions
• traffic network equilibrium problem

2010 Mathematics Subject Classifications:

• 49K40
• 90C31
• 91B50

Acknowledgments

The authors would like to thank anonymous referees for their valuable remarks and suggestions which have helped us improve the paper.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This research is funded by Vietnam National Foundation for Science and Technology Development (NAFOSTED) [grant number 101.01-2017.18].