On Lipschitz continuity of approximate solutions to set-valued equilibrium problems via nonlinear scalarization

Abstract

In this paper, we consider parametric set-valued equilibrium problems in normed spaces. By virtue of the Gerstewitz nonlinear scalarization function along with relaxed concavity assumptions, we obtain the Lipschitz continuity property of solution maps to such problems. The treatment and obtained results for these problems are new and different from the existing ones in the literature. We apply the main results to the Browder variational inclusion to illustrate for their applicability.

Keywords:

• Lipschitz continuity
• approximate solution
• equilibrium problem
• Browder variational inclusion
• nonlinear scalarization

AMS CLASSIFICATIONs:

• 49K40
• 90C31
• 91B50

Acknowledgments

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

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This is a result of the project under Grant number B2021-TCT-02 supported by The Ministry of Education and Training of Viet Nam.