The minimal displacement problem in the space l ∞
Krzysztof Bolibok (2012)
Open Mathematics
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We give a lower bound for the minimal displacement characteristic in the space l ∞.
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Krzysztof Bolibok (2012)
Open Mathematics
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We give a lower bound for the minimal displacement characteristic in the space l ∞.
Łukasz Piasecki (2015)
Annales UMCS, Mathematica
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The aim of this paper is to show that for every Banach space (X, || · ||) containing asymptotically isometric copy of the space c0 there is a bounded, closed and convex set C ⊂ X with the Chebyshev radius r(C) = 1 such that for every k ≥ 1 there exists a k-contractive mapping T : C → C with [...] for any x ∊ C.
Tomasz Downarowicz (2011)
Colloquium Mathematicae
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We construct an example of two commuting homeomorphisms S, T of a compact metric space X such that the union of all minimal sets for S is disjoint from the union of all minimal sets for T. In other words, there are no common minimal points. This answers negatively a question posed in [C-L]. We remark that Furstenberg proved the existence of "doubly recurrent" points (see [F]). Not only are these points recurrent under both S and T, but they recur along the same sequence of powers. Our...
A. I. Ban, S. G. Gal (2002)
Archivum Mathematicum
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New contributions concerning the minimal displacement of points under mappings (defect of fixed point) are obtained.
L Moser (1959)
Acta Arithmetica
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