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

Author

Listed:
  • John Cotrina

    (Universidad del Pacífico)

  • Michel Théra

    (Université de Limoges
    Federation University Australia)

  • Javier Zúñiga

    (Universidad del Pacífico)

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.

Suggested Citation

  • John Cotrina & Michel Théra & Javier Zúñiga, 2020. "An Existence Result for Quasi-equilibrium Problems via Ekeland’s Variational Principle," Journal of Optimization Theory and Applications, Springer, vol. 187(2), pages 336-355, November.
    • Handle: RePEc:spr:joptap:v:187:y:2020:i:2:d:10.1007_s10957-020-01764-0
    DOI: 10.1007/s10957-020-01764-0
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    References listed on IDEAS

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    1. Massimiliano Giuli, 2017. "Cyclically monotone equilibrium problems and Ekeland’s principle," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 40(1), pages 231-242, November.
    2. M. Castellani & M. Giuli, 2010. "On Equivalent Equilibrium Problems," Journal of Optimization Theory and Applications, Springer, vol. 147(1), pages 157-168, October.
    3. D. Aussel & J. Cotrina, 2013. "Quasimonotone Quasivariational Inequalities: Existence Results and Applications," Journal of Optimization Theory and Applications, Springer, vol. 158(3), pages 637-652, September.
    4. Marco Castellani & Massimiliano Giuli & Massimo Pappalardo, 2018. "A Ky Fan Minimax Inequality for Quasiequilibria on Finite-Dimensional Spaces," Journal of Optimization Theory and Applications, Springer, vol. 179(1), pages 53-64, October.
    5. Tian, Guoqiang & Zhou, Jianxin, 1995. "Transfer continuities, generalizations of the Weierstrass and maximum theorems: A full characterization," Journal of Mathematical Economics, Elsevier, vol. 24(3), pages 281-303.
    6. M. Bianchi & S. Schaible, 2000. "An Extension of Pseudolinear Functions and Variational Inequality Problems," Journal of Optimization Theory and Applications, Springer, vol. 104(1), pages 59-71, January.
    7. M. Castellani & M. Giuli, 2013. "Refinements of existence results for relaxed quasimonotone equilibrium problems," Journal of Global Optimization, Springer, vol. 57(4), pages 1213-1227, December.
    8. M. Alizadeh & M. Bianchi & N. Hadjisavvas & R. Pini, 2014. "On cyclic and $$n$$ n -cyclic monotonicity of bifunctions," Journal of Global Optimization, Springer, vol. 60(4), pages 599-616, December.
    9. John Cotrina & Javier Zúñiga, 2019. "Quasi-equilibrium problems with non-self constraint map," Journal of Global Optimization, Springer, vol. 75(1), pages 177-197, September.
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