Existence results for -quasimonotone equilibrium problems in convex metric spaces

Abstract

This paper deals with equilibrium problems in the setting of metric spaces with a continuous convex structure. We extend Fan’s 1984 KKM theorem to convex metric spaces in order to employ some weak coercivity conditions to establish existence results for suitable local Minty equilibrium problems, where the involved bifunctions are -quasimonotone. By an approach which is based on the concept of the strong -sign property for bifunctions, we obtain existence results for equilibrium problems which generalize some results in the literature.

Keywords:

• Convex metric space
• equilibrium problem
• -quasimonotone
• strong -sign property

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Erratum

Acknowledgements

The authors are very grateful to the anonymous referees for their valuable remarks which helped to improve significantly the paper.

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was carried out while the first author was visiting the Department of Mathematics, Arak University, Iran, from September 2015 to February 2016. P. Q. Khanh work was supported by the National Foundation for Science and Technology Development (NAFOSTED) of Vietnam under [grant number 101.01-2014.62].