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Solutions and Approximate Solutions of Quasi-Equilibrium Problems in Banach Spaces

Author

Listed:
  • Boualem Alleche

    (Université de Médéa)

  • Vicenţiu D. Rădulescu

    (King Abdulaziz University
    Institute of Mathematics “Simion Stoilow” of the Romanian Academy)

Abstract

This paper deals with quasi-equilibrium problems in the setting of real Banach spaces. By a fixed point theory approach, we obtain existence results under mild conditions of continuity, improving some previous results in this area. By a selection theory approach, we make use of the Michael selection theorem to overcome the separability of the Banach spaces and generalize some results obtained recently in the literature. Finally, we deal with the existence of approximate solutions for quasi-equilibrium problems, and by arguments combining selection theory and fixed point theory, we obtain some qualitative results for quasi-equilibrium problems involving sub-lower semicontinuous set-valued mappings.

Suggested Citation

  • Boualem Alleche & Vicenţiu D. Rădulescu, 2016. "Solutions and Approximate Solutions of Quasi-Equilibrium Problems in Banach Spaces," Journal of Optimization Theory and Applications, Springer, vol. 170(2), pages 629-649, August.
    • Handle: RePEc:spr:joptap:v:170:y:2016:i:2:d:10.1007_s10957-015-0854-1
    DOI: 10.1007/s10957-015-0854-1
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    References listed on IDEAS

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    1. I. V. Konnov & S. Schaible, 2000. "Duality for Equilibrium Problems under Generalized Monotonicity," Journal of Optimization Theory and Applications, Springer, vol. 104(2), pages 395-408, February.
    2. Gábor Kassay, 2010. "On Equilibrium Problems," Springer Optimization and Its Applications, in: Altannar Chinchuluun & Panos M. Pardalos & Rentsen Enkhbat & Ider Tseveendorj (ed.), Optimization and Optimal Control, pages 55-83, Springer.
    3. Paolo Cubiotti & Jen-Chih Yao, 2010. "Nash equilibria of generalized games in normed spaces without upper semicontinuity," Journal of Global Optimization, Springer, vol. 46(4), pages 509-519, April.
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    Cited by:

    1. Boualem Alleche & Vicenţiu D. Rădulescu, 2017. "Further on Set-Valued Equilibrium Problems and Applications to Browder Variational Inclusions," Journal of Optimization Theory and Applications, Springer, vol. 175(1), pages 39-58, October.
    2. Mircea Balaj, 2022. "Scalar and vector equilibrium problems with pairs of bifunctions," Journal of Global Optimization, Springer, vol. 84(3), pages 739-753, November.
    3. 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.

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