Abstract
The main result is a fixed point theorem for compositions of chain faithful multifunctions (Corollary 2.3). The theorem is then applied to get sufficient conditions for the fixed point property of the product of two partially ordered sets.
Similar content being viewed by others
References
S. Abian andA. B. Brown,A theorem on partially ordered sets, with applications to fixed point theorems, Canad. J. Math.13 (1961), 78–82.
T. S. Fofanova,On the fixed point property of partially ordered sets, Coil. Math. Soc. János Bolyai,33. Contributions to Lattice Theory, Szeged (Hungary) 1980, 401–406.
H.Höft,Order preserving selections for multifunctions, Contributions to General Algebra 5.
I. Rival,The problem of fixed points in ordered sets, Ann. Discrete Math.8 (1980), 283–292.
I. Rival,The fixed point property, Order2 (1985), 219–221.
A. Rutkowski,Multifunctions and the fixed point property for products of ordered sets, Order2 (1985), 61–67.
R. E. Smithson,Fixed points of order preserving multifunctions, Proc. A.M.S. Vol.28 (1971), 304–310.
J. W. Walker,Isotone relations and the fixed point property for posets, Discrete Math.48 (1984), 275–288.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Höft, M. A fixed point theorem for multifunctions and an application. Algebra Universalis 24, 283–288 (1987). https://doi.org/10.1007/BF01195267
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF01195267