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Approximate solutions of quasiequilibrium problems in Banach spaces

Author

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  • M. Castellani

    (University of L’Aquila)

  • M. Giuli

    (University of L’Aquila)

Abstract

In this note we show that a recent existence result on quasiequilibrium problems, which seems to improve deeply some well-known results, is not correct. We exhibit a counterexample and we furnish a generalization of a lemma about continuous $$\varepsilon $$ ε -minimizers of quasiconvex functions depending on a parameter. This allows to establish an existence result of approximate solutions of quasiequilibrium problems.

Suggested Citation

  • M. Castellani & M. Giuli, 2016. "Approximate solutions of quasiequilibrium problems in Banach spaces," Journal of Global Optimization, Springer, vol. 64(3), pages 615-620, March.
    • Handle: RePEc:spr:jglopt:v:64:y:2016:i:3:d:10.1007_s10898-015-0386-0
    DOI: 10.1007/s10898-015-0386-0
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    References listed on IDEAS

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    1. Bigi, Giancarlo & Castellani, Marco & Pappalardo, Massimo & Passacantando, Mauro, 2013. "Existence and solution methods for equilibria," European Journal of Operational Research, Elsevier, vol. 227(1), pages 1-11.
    2. Charalambos D. Aliprantis & Kim C. Border, 2006. "Infinite Dimensional Analysis," Springer Books, Springer, edition 0, number 978-3-540-29587-7, December.
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    Cited by:

    1. 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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