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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Fixed points
of contractive multivalued maps


Authors: L. Górniewicz, S. A. Marano and M. Slosarski
Journal: Proc. Amer. Math. Soc. 124 (1996), 2675-2683
MSC (1991): Primary 47H10, 47H04
MathSciNet review: 1317038
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Abstract: For a class of contractive multivalued maps defined on a complete absolute retract and with closed bounded values, the set of fixed points is proved to be an absolute retract. This result unifies and extends to arbitrary absolute retracts both Theorem 1 by Ricceri [Atti Accad. Naz. Lincei Rend. Cl.Sci. Fis. Mat. Natur. (8) 81 (1987), 283--286] and Theorem 1 by Bressan, Cellina, and Fryszkowski [Proc. Amer. Math. Soc. 112 (1991), 413--418].


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Additional Information

L. Górniewicz
Affiliation: Institute of Mathematics, University Nicholas Copernicus, Chopina 12/18, 87-100 Toruń, Poland
Email: gorn@mat.uni.torun.pl

S. A. Marano
Affiliation: Department of Mathematics, University of Catania, Viale A. Doria 6, 95125 Catania, Italy
Email: marano@dipmat.unict.it

M. Slosarski
Affiliation: Institute of Mathematics, University Nicholas Copernicus, Chopina 12/18, 87-100 Toruń, Poland

DOI: http://dx.doi.org/10.1090/S0002-9939-96-03265-0
PII: S 0002-9939(96)03265-0
Keywords: Contractive multivalued map, fixed point, absolute retract
Received by editor(s): November 7, 1994
Received by editor(s) in revised form: January 9, 1995
Additional Notes: This paper was performed in part while the second author was visiting the Institute of Mathematics, University Nicholas Copernicus, Toruń
Communicated by: Palle E. T. Jorgensen
Article copyright: © Copyright 1996 American Mathematical Society