Some topological properties of the 1-set contractions

Domínguez Benavides, Tomás

doi:10.1090/S0002-9939-1985-0770531-5

Some topological properties of the $1$-set contractions
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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 ${\Sigma _1}(C)$.

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Some generic properties of

-nonexpansive operators

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