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The finite intersection property for equilibrium problems

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Abstract

The “finite intersection property” for bifunctions is introduced and its relationship with generalized monotonicity properties is studied. Some characterizations are considered involving the Minty equilibrium problem. Also, some results concerning existence of equilibria and quasi-equilibria are established recovering several results in the literature. Furthermore, we give an existence result for generalized Nash equilibrium problems and variational inequality problems.

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Notes

  1. As in the book Functional Analysis by Rudin, a topological vector space includes in its definition that the underlying topology is Hausdorff separated

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Acknowledgements

The authors would like to thank Didier Aussel for his valuable suggestions in Propositions 2, 3, 6 and , Corollary 3 and also Example 4. We also wish to thank the referee for his/her helpful comments and suggestions.

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Authors and Affiliations

  1. Universidad del Pacífico, Lima, Peru

    John Cotrina

  2. Universidad de O’Higgins, Rancagua, Chile

    Anton Svensson

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  1. John Cotrina
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  2. Anton Svensson
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Correspondence to John Cotrina.

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Cotrina, J., Svensson, A. The finite intersection property for equilibrium problems. J Glob Optim 79, 941–957 (2021). https://doi.org/10.1007/s10898-020-00961-5

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  • DOI: https://doi.org/10.1007/s10898-020-00961-5

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