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A fixed point theorem without convexity

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 hypotheses, 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. "A fixed point theorem without convexity," UC3M Working papers. Economics 6022, Universidad Carlos III de Madrid. Departamento de Economía.
    • Handle: RePEc:cte:werepe:6022
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    Keywords

    Fixed point theorems;

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