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Densely Defined Equilibrium Problems

Author

Listed:
  • Szilárd László

    (Technical University of Cluj-Napoca)

  • Adrian Viorel

    (Technical University of Cluj-Napoca
    Babeş-Bolyai University Cluj-Napoca)

Abstract

In the present work, we deal with set-valued equilibrium problems, for which we provide sufficient conditions for the existence of a solution. The conditions, that we consider, are imposed not on the whole domain, but rather on a self-segment-dense subset of it, a special type of dense subset. As an application, we obtain a generalized Debreu–Gale–Nikaïdo-type theorem, with a considerably weakened Walras law in its hypothesis. Furthermore, we consider a noncooperative $$n$$ n -person game and prove the existence of a Nash equilibrium, under assumptions that are less restrictive than the classical ones.

Suggested Citation

  • Szilárd László & Adrian Viorel, 2015. "Densely Defined Equilibrium Problems," Journal of Optimization Theory and Applications, Springer, vol. 166(1), pages 52-75, July.
    • Handle: RePEc:spr:joptap:v:166:y:2015:i:1:d:10.1007_s10957-014-0702-8
    DOI: 10.1007/s10957-014-0702-8
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    References listed on IDEAS

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    1. K. L. Lin & D. P. Yang & J. C. Yao, 1997. "Generalized Vector Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 92(1), pages 117-125, January.
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    Cited by:

    1. Somaye Jafari & Ali Farajzadeh & Sirous Moradi, 2016. "Locally Densely Defined Equilibrium Problems," Journal of Optimization Theory and Applications, Springer, vol. 170(3), pages 804-817, September.
    2. Szilárd László, 2016. "Vector Equilibrium Problems on Dense Sets," Journal of Optimization Theory and Applications, Springer, vol. 170(2), pages 437-457, August.
    3. 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.
    4. Ayed E. Hashoosh & Mohsen Alimohammady & M. K. Kalleji, 2016. "Existence Results for Some Equilibrium Problems Involving -Monotone Bifunction," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2016, pages 1-5, February.

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