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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Some topological properties of the $ 1$-set contractions


Author: Tomás Domínguez Benavides
Journal: Proc. Amer. Math. Soc. 93 (1985), 252-254
MSC: Primary 47H09; Secondary 58C30
MathSciNet review: 770531
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Abstract: Let $ C$ be a bounded closed convex subset of a Banach space $ X$. It is shown that, in the category sense, almost all $ 1$-set-contractions $ f:C \to C$ are condensing. To know how the condensing mappings are scattered in the set $ {\Sigma _1}(C)$ of $ 1$-set-contractions it is proved that the set of noncondensing mappings is dense in $ {\Sigma _1}(C)$.


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DOI: https://doi.org/10.1090/S0002-9939-1985-0770531-5
Keywords: $ k$-set-contractions, Baire category, condensing mappings, fixed points, residual subset
Article copyright: © Copyright 1985 American Mathematical Society