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Abstract convexity, some relations and applications

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  • Llinarès, Juan Vicente

Abstract

The aim of this paper is to analyze the relationship between different notions of abstract convexity structures that we can find in the literature in connection with the problem of the existence of continuous selections and fixed points to correspondences. Mainly we will focus in the notion of mc-spaces, which was introduced in LLinares (1994, 1997), and its relationship with c-spaces (Horvath, 1991), simplicial convexity (Bielawski, 1987) an order convexity (used in Horvath and LLinares, 1996), B'-simplicial convexity and L-spaces (Ben-El-Mechaiekh and al., 1997). Moreover, in the context of mc-spaces, a characterization result of non-empty finite intersection in the line of the Knaster-Kuratowski-Mazurkievicz lemma, some consequences of it and some generalizations of Browder's existence of continuous selection and fixed point theorem are presented.

Suggested Citation

  • Llinarès, Juan Vicente, 1998. "Abstract convexity, some relations and applications," CEPREMAP Working Papers (Couverture Orange) 9803, CEPREMAP.
    • Handle: RePEc:cpm:cepmap:9803
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    File URL: http://www.cepremap.fr/depot/couv_orange/co9803.pdf
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    References listed on IDEAS

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    1. Llinares, Juan-Vicente, 1998. "Unified treatment of the problem of existence of maximal elements in binary relations: a characterization," Journal of Mathematical Economics, Elsevier, vol. 29(3), pages 285-302, April.
    2. 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).
    3. Juan Vicente Llinares Císcar, 1995. "Existence Of Maximal Elements In A Binary Relation Relaxing The Convexity Condition," Working Papers. Serie AD 1995-10, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
    4. Horvath, Charles D. & Ciscar, Juan Vicente Llinares, 1996. "Maximal elements and fixed points for binary relations on topological ordered spaces," Journal of Mathematical Economics, Elsevier, vol. 25(3), pages 291-306.
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    Cited by:

    1. J. V. Llinares, 2000. "Existence of Equilibrium in Generalized Games with Abstract Convexity Structure," Journal of Optimization Theory and Applications, Springer, vol. 105(1), pages 149-160, April.

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