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Abstract Convexity and Fixed Points

Author

Listed:
  • Ben-El-Mechaiekh, H.
  • Chebbi, S.
  • Florenzano, M.
  • Llinares, J.-V.

Abstract

The purpose of this paper is to extend Himmelberg's fixed point theorem replacing the usual convexity in topological vector spaces by an abstract topological notion of convexity which generalizes classical convexity as well as several metric convexity structures found in the literature. We prove the existence, under weak hypothese, of a fixed point for a compact approachable map and we provide sufficient conditions under which this result applies to maps whose values are convex in the abstract sense mentionned above.

Suggested Citation

  • Ben-El-Mechaiekh, H. & Chebbi, S. & Florenzano, M. & Llinares, J.-V., 1997. "Abstract Convexity and Fixed Points," Papiers d'Economie Mathématique et Applications 97.87, Université Panthéon-Sorbonne (Paris 1).
    • Handle: RePEc:fth:pariem:97.87
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    Citations

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    Cited by:

    1. Pascal Gourdel & Hakim Hammami, 2007. "Applications of generalized Ky Fan's matching theorem in minimax and variational inequality," Post-Print halshs-00204627, HAL.
    2. Souhail Chebbi & Pascal Gourdel & Hakim Hammami, 2006. "A Generalization of Fan's Matching Theorem," Cahiers de la Maison des Sciences Economiques b06060a, Université Panthéon-Sorbonne (Paris 1), revised Jan 2008.
    3. M. Carmen Sánchez & Juan-Vicente Llinares & Begoña Subiza, 2003. "A KKM-result and an application for binary and non-binary choice functions," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 21(1), pages 185-193, January.
    4. Souhail Chebbi & Pascal Gourdel & Hakim Hammami, 2008. "A generalization of Fan's matching theorem," PSE-Ecole d'économie de Paris (Postprint) hal-00756058, HAL.
    5. Llinarès, Juan Vicente, 1998. "Existence of equilibrium in generalized games with non-convex strategy spaces," CEPREMAP Working Papers (Couverture Orange) 9801, CEPREMAP.
    6. Xie Ding, 2010. "New systems of generalized vector quasi-equilibrium problems in product FC-spaces," Journal of Global Optimization, Springer, vol. 46(1), pages 133-146, January.
    7. Souhail Chebbi & Pascal Gourdel & Hakim Hammami, 2008. "A generalization of Fan's matching theorem," Post-Print hal-00756058, HAL.
    8. Llinarès, Juan Vicente, 1998. "Abstract convexity, some relations and applications," CEPREMAP Working Papers (Couverture Orange) 9803, CEPREMAP.
    9. Souhail Chebbi & Pascal Gourdel & Hakim Hammami, 2008. "A generalization of Fan's matching theorem," Post-Print halshs-00118929, HAL.
    10. Gayatri Pany & Ram N. Mohapatra & Sabyasachi Pani, 2018. "Solution of a class of equilibrium problems and variational inequalities in FC spaces," Annals of Operations Research, Springer, vol. 269(1), pages 565-582, October.
    11. Xie Ding, 2012. "Equilibrium existence theorems for multi-leader-follower generalized multiobjective games in FC-spaces," Journal of Global Optimization, Springer, vol. 53(3), pages 381-390, July.

    More about this item

    Keywords

    MATHEMATICS;

    JEL classification:

    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium

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