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Refinements of existence results for relaxed quasimonotone equilibrium problems

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Abstract

We consider a general equilibrium problem in a normed vector space setting and we establish sufficient conditions for the existence of solutions in compact and non compact cases. Our approach is based on the concept of upper sign property for bifunctions, which turns out to be a very weak assumption for equilibrium problems. In the framework of variational inequalities, this notion coincides with the upper sign continuity for a set-valued operator introduced by Hadjisavvas. More in general, it allows to strengthen a number of existence results for the class of relaxed \(\mu \)-quasimonotone equilibrium problems.

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Acknowledgments

Authors wish to thank the anonymous referees for their useful comments and suggestions, which allow to improve the presentation of this paper.

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  1. Department of Information Engineering, Computer Science and Mathematics, L’Aquila, Italy

    M. Castellani & M. Giuli

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  1. M. Castellani
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  2. M. Giuli
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Correspondence to M. Giuli.

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Castellani, M., Giuli, M. Refinements of existence results for relaxed quasimonotone equilibrium problems. J Glob Optim 57, 1213–1227 (2013). https://doi.org/10.1007/s10898-012-0021-2

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