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Results tagged with fixed-point-theorems
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user 10583
A fixed-point theorem is a result saying that a function $F$ will have at least one fixed point (a point $x$ for which $F(x) = x$), under some conditions on $F$ that can be stated in general terms.
7
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Nonexpansive multi-valued maps in $\ell^2$
Let $C$ be a nonempty bounded closed convex subset, say the unit ball, of $\ell^2(\mathbb{N})$. Let $T: C\to 2^C$ be a map such that $T(x)$ is nonempty closed for each $x$, and that $$D(Tx,Ty)\le \|x- …
- 744
1
vote
Variants of point fixed theorem
Let X be the predual of E. If the dual of every separable subspace of X is separable, then C contains a point that is fixed by EVERY weak* continuous affine isometry of C into C.
This is Theorem 2 in …
- 744