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Refinements of existence results for relaxed quasimonotone equilibrium problems

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  • M. Castellani
  • M. Giuli

Abstract

We consider a general equilibrium problem in a normed vector space setting and we establish sufficient conditions for the existence of solutions in compact and non compact cases. Our approach is based on the concept of upper sign property for bifunctions, which turns out to be a very weak assumption for equilibrium problems. In the framework of variational inequalities, this notion coincides with the upper sign continuity for a set-valued operator introduced by Hadjisavvas. More in general, it allows to strengthen a number of existence results for the class of relaxed $$\mu $$ -quasimonotone equilibrium problems. Copyright Springer Science+Business Media New York 2013

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  • 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.
    • Handle: RePEc:spr:jglopt:v:57:y:2013:i:4:p:1213-1227
    DOI: 10.1007/s10898-012-0021-2
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    References listed on IDEAS

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    1. D. Aussel & N. Hadjisavvas, 2004. "On Quasimonotone Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 121(2), pages 445-450, May.
    2. M. Bianchi & R. Pini, 2005. "Coercivity Conditions for Equilibrium Problems," Journal of Optimization Theory and Applications, Springer, vol. 124(1), pages 79-92, January.
    3. M. R. Bai & N. Hadjisavvas, 2008. "Relaxed Quasimonotone Operators and Relaxed Quasiconvex Functions," Journal of Optimization Theory and Applications, Springer, vol. 138(3), pages 329-339, September.
    4. M. Bianchi & N. Hadjisavvas & S. Schaible, 2004. "Minimal Coercivity Conditions and Exceptional Families of Elements in Quasimonotone Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 122(1), pages 1-17, July.
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    Cited by:

    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. Didier Aussel & Parin Chaipunya, 2024. "Variational and Quasi-Variational Inequalities Under Local Reproducibility: Solution Concept and Applications," Journal of Optimization Theory and Applications, Springer, vol. 203(2), pages 1531-1563, November.
    3. Cholamjiak, Watcharaporn & Dutta, Hemen & Yambangwai, Damrongsak, 2021. "Image restorations using an inertial parallel hybrid algorithm with Armijo linesearch for nonmonotone equilibrium problems," Chaos, Solitons & Fractals, Elsevier, vol. 153(P1).
    4. Yekini Shehu & Lulu Liu & Xiaolong Qin & Qiao-Li Dong, 2022. "Reflected Iterative Method for Non-Monotone Equilibrium Problems with Applications to Nash-Cournot Equilibrium Models," Networks and Spatial Economics, Springer, vol. 22(1), pages 153-180, March.
    5. 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.
    6. 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.
    7. M. Castellani & M. Giuli, 2019. "A coercivity condition for nonmonotone quasiequilibria on finite-dimensional spaces," Journal of Global Optimization, Springer, vol. 75(1), pages 163-176, September.
    8. 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.
    9. John Cotrina & Anton Svensson, 2021. "The finite intersection property for equilibrium problems," Journal of Global Optimization, Springer, vol. 79(4), pages 941-957, April.

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