An approach of equilibrium problems based on selection theorems

Abstract

In the study of the existence of solutions to equilibrium problems, the intersection theorems are useful tools of investigation. In this paper, the proofs combine selection results with intersection theorems. An important feature of our results is that they are obtained without the standard equilibrium condition.

Keywords:

• Equilibrium problem
• continuous selection
• quasi-equilibrium problem
• variational-like inequality problem

Mathematics Subject Classifications:

• 49J53
• 47J20
• 54C65

Acknowledgments

We would like to thank the two anonymous referees for their insightful comments which led to an improved version of the paper.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The research of Marco Castellani and Massimiliano Giuli is partially supported by the ‘INdAM – GNAMPA Project’, codice CUP E53C23001670001.