Some topological properties of the $1$-set contractions
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- by Tomás Domínguez Benavides PDF
- Proc. Amer. Math. Soc. 93 (1985), 252-254 Request permission
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 ${\Sigma _1}(C)$.References
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Additional Information
- © Copyright 1985 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 93 (1985), 252-254
- MSC: Primary 47H09; Secondary 58C30
- DOI: https://doi.org/10.1090/S0002-9939-1985-0770531-5
- MathSciNet review: 770531