Lipschitz continuity of an approximate solution mapping for parametric set-valued vector equilibrium problems

Abstract

The purpose of this paper is to generalize and improve some topological properties of solutions set to the set-valued vector equilibrium problems by using the scalar characterization method. Moreover, the Lipschitz continuity of an approximate solution mapping for the parametric set-valued vector equilibrium problems is studied.

Keywords:

• set-valued vector equilibrium problem
• approximate solution mapping
• scalarization method
• Lipschitz continuity

AMS Subject Classifications:

• 49J40
• 49K40
• 90C31

Acknowledgements

The authors are grateful to the editor and reviewers for their valuable comments and suggestions that allowed us to improve the original presentation. We also thank Prof. B. Mordokhuvich and M. Shahryari for their helpful remarks.

Notes

No potential conflict of interest was reported by the authors.