On affine subspaces that illuminate a convex set.
Bezdek, Károly (1994)
Beiträge zur Algebra und Geometrie
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Bezdek, Károly (1994)
Beiträge zur Algebra und Geometrie
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J. Pym (1993)
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Janusz Matkowski (2003)
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The class of all functions f:(0,∞) → (0,∞) which are continuous at least at one point and affine with respect to the logarithmic mean is determined. Some related results concerning the functions convex with respect to the logarithmic mean are presented.
Zygfryd Kominek, T. Zgraja (1999)
Acta Universitatis Carolinae. Mathematica et Physica
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Leichtweiss, Kurt (1999)
Beiträge zur Algebra und Geometrie
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D. G. Keselman (1986)
Commentationes Mathematicae Universitatis Carolinae
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D. Helmer (1980)
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Leichtweiß, Kurt (2002)
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Józef Joachim Telega (1977)
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Janko Marovt (2006)
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Let 𝒳 be a compact Hausdorff space which satisfies the first axiom of countability, I = [0,1] and 𝓒(𝒳,I) the set of all continuous functions from 𝒳 to I. If φ: 𝓒(𝒳,I) → 𝓒(𝒳,I) is a bijective affine map then there exists a homeomorphism μ: 𝒳 → 𝒳 such that for every component C in 𝒳 we have either φ(f)(x) = f(μ(x)), f ∈ 𝓒(𝒳,I), x ∈ C, or φ(f)(x) = 1-f(μ(x)), f ∈ 𝓒(𝒳,I), x ∈ C.