A fixed point theorem without convexity

H. Ben-El-Mechaiekh, S. Chebbi, Monique Florenzano and Juan Vicente Llinares

UC3M Working papers. Economics from Universidad Carlos III de Madrid. Departamento de Economía

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.

Keywords: Fixed; point; theorems; Generalized; convexity; Compact; correspondences; Approachable; correspondences (search for similar items in EconPapers)
Date: 1997-04
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Persistent link: https://EconPapers.repec.org/RePEc:cte:werepe:6022

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