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Fixed Point and Equilibrium Theorems in a Generalized Convexity Framework

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  • Monica Patriche

    (University of Bucharest)

Abstract

We study the fixed point property of set-valued maps and the existence of equilibria in the framework of $\mathbb{B}$ -convexity, recently defined by W. Briec and Ch. Horvath. We introduce some classes of the set-valued maps with generalized convexity and prove continuous selection and fixed point properties for them. Finally, we obtain results concerning the existence of quasi-equilibria for W.K. Kim’s new model.

Suggested Citation

  • Monica Patriche, 2013. "Fixed Point and Equilibrium Theorems in a Generalized Convexity Framework," Journal of Optimization Theory and Applications, Springer, vol. 156(3), pages 701-715, March.
    • Handle: RePEc:spr:joptap:v:156:y:2013:i:3:d:10.1007_s10957-012-0133-3
    DOI: 10.1007/s10957-012-0133-3
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    References listed on IDEAS

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    1. Yannelis, Nicholas C. & Prabhakar, N. D., 1983. "Existence of maximal elements and equilibria in linear topological spaces," Journal of Mathematical Economics, Elsevier, vol. 12(3), pages 233-245, December.
    2. Shafer, Wayne & Sonnenschein, Hugo, 1975. "Equilibrium in abstract economies without ordered preferences," Journal of Mathematical Economics, Elsevier, vol. 2(3), pages 345-348, December.
    3. Vives, Xavier, 1990. "Nash equilibrium with strategic complementarities," Journal of Mathematical Economics, Elsevier, vol. 19(3), pages 305-321.
    4. Aliprantis, Charalambos D. & Florenzano, Monique & Tourky, Rabee, 2004. "General equilibrium analysis in ordered topological vector spaces," Journal of Mathematical Economics, Elsevier, vol. 40(3-4), pages 247-269, June.
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    Cited by:

    1. Carlos Hervés-Beloso & Monica Patriche, 2014. "A Fixed-Point Theorem and Equilibria of Abstract Economies with Weakly Upper Semicontinuous Set-Valued Maps," Journal of Optimization Theory and Applications, Springer, vol. 163(3), pages 719-736, December.

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