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Equilibrium versions of variational principles in quasi-metric spaces and the robust trap problem

Author

Listed:
  • Jing-Hui Qiu

    (Soochow University)

  • Fei He

    (THU - Tsinghua University [Beijing])

  • Antoine Soubeyran

    (AMSE - Aix-Marseille Sciences Economiques - EHESS - École des hautes études en sciences sociales - AMU - Aix Marseille Université - ECM - École Centrale de Marseille - CNRS - Centre National de la Recherche Scientifique)

Abstract

Using a pre-order principle in [Qiu JH. A pre-order principle and set-valued Ekeland variational principle. J Math Anal Appl. 2014;419:904–937], we establish a general equilibrium version of set-valued Ekeland variational principle (denoted by EVP), where the objective bimap is defined on the product of left-complete quasi-metric spaces and taking values in a quasi-order linear space, and the perturbation consists of the quasi-metric and a positive vector . Here, the ordering is only to be -closed, which is strictly weaker than to be topologically closed. From the general equilibrium version, we deduce a number of particular equilibrium versions of EVP with set-valued bimaps or with vector-valued bimap. As applications of the equilibrium versions of EVP, we present several interesting results on equilibrium problems, vector optimization and fixed point theory in the setting of quasi-metric spaces. These results extend and improve the related known results. Using the obtained EVPs, we further study the existence and the robustness of traps in Behavioural Sciences.

Suggested Citation

  • Jing-Hui Qiu & Fei He & Antoine Soubeyran, 2017. "Equilibrium versions of variational principles in quasi-metric spaces and the robust trap problem," Post-Print hal-02084464, HAL.
    • Handle: RePEc:hal:journl:hal-02084464
    DOI: 10.1080/02331934.2017.1387257
    Note: View the original document on HAL open archive server: https://amu.hal.science/hal-02084464
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    References listed on IDEAS

    as
    1. Truong Q. Bao & Boris S. Mordukhovich & Antoine Soubeyran, 2015. "Minimal points, variational principles, and variable preferences in set optimization," Post-Print hal-01457319, HAL.
    2. Phan Khanh & Dinh Quy, 2013. "Versions of Ekeland’s variational principle involving set perturbations," Journal of Global Optimization, Springer, vol. 57(3), pages 951-968, November.
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