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Existence Of Maximal Elements In A Binary Relation Relaxing The Convexity Condition

Author

Listed:
  • Juan Vicente Llinares Císcar

    (Universidad de Murcia)

Abstract

In this paper we relax the convexity condition in some classical results on the existence of maximal elements in binary relations in order to generalize them. To do this, we replace the linear segments in the usual convexity with a family of previously fixed paths joining up each two points. From these paths, we introduce a family of sets which generalizes the usual convex sets, and in this context we extend Sonnenschein's theorem on the existence of maximal elements and Browder's theorem on the existence of continuous selection and f ixed point to correspondences.

Suggested Citation

  • 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).
    • Handle: RePEc:ivi:wpasad:1995-10
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    File URL: http://www.ivie.es/downloads/docs/wpasad/wpasad-1995-10.pdf
    File Function: Fisrt version / Primera version, 1995
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    Cited by:

    1. Llinarès, Juan Vicente, 1998. "Abstract convexity, some relations and applications," CEPREMAP Working Papers (Couverture Orange) 9803, CEPREMAP.

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