Fixed points of contractive multivalued maps |
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| Authors: | L Gó rniewicz S A Marano M Slosarski |
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| Institution: | Institute of Mathematics, University Nicholas Copernicus, Chopina 12/18, 87-100 Torun, Poland ; Department of Mathematics, University of Catania, Viale A. Doria 6, 95125 Catania, Italy ; Institute of Mathematics, University Nicholas Copernicus, Chopina 12/18, 87-100 Torun, Poland |
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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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| Keywords: | Contractive multivalued map fixed point absolute retract |
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