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An Existence Result for Quasi-equilibrium Problems via Ekeland’s Variational Principle

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Abstract

This paper deals with the existence of solutions to equilibrium and quasi-equilibrium problems without any convexity assumption. Coverage includes some equivalences to the Ekeland variational principle for bifunctions and basic facts about transfer lower continuity. An application is given to systems of quasi-equilibrium problems.

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Notes

  1. Introduced by R. Baire, see [31] and the references therein.

  2. \({\mathrm{Fix}}(K)\) denotes the set of fixed points of K.

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Acknowledgements

We wish to thank the referees and the associate editor for their helpful comments and suggestions. Research of M. Théra is supported by the Australian Research Council (ARC) Grant DP160100854 and benefited from the support of the FMJH Program PGMO and from the support of EDF.

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Authors and Affiliations

  1. Universidad del Pacífico, Lima, Peru

    John Cotrina & Javier Zúñiga

  2. XLIM UMR-CNRS 7252, Université de Limoges, Limoges, France

    Michel Théra

  3. Centre for Informatics and Applied Optimization, School of Science, Engineering and Information Technology, Federation University Australia, Ballarat, Australia

    Michel Théra

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  1. John Cotrina
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  2. Michel Théra
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  3. Javier Zúñiga
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Correspondence to John Cotrina.

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Cotrina, J., Théra, M. & Zúñiga, J. An Existence Result for Quasi-equilibrium Problems via Ekeland’s Variational Principle. J Optim Theory Appl 187, 336–355 (2020). https://doi.org/10.1007/s10957-020-01764-0

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