Abstract
Let us call a sequence of functions
an inequality measure, if it satisfies strict Schur convexity, i.e.,
-
(1)
In(Bx) < In(Bx) for all x ∈ IR n+ , x ≠ (a, …, a) and for all bistochastic matrices B such that Bx is not a permutation of the components of x,
In(Bx) = In(Bx) otherwise, and
-
(2)
In(a, …, a) = 0 for all a *#x2208; IR+ (normalization), and
-
(3)
In(x1, …, xn) ≤ In+1(x1, …, xn, 0) for all x ∈ IR n+ (extension).
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© 1987 Birkhäuser Verlag Basel
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Eichhorn, W. (1987). Three Problems. In: Walter, W. (eds) General Inequalities 5. International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik Série internationale d’Analyse numérique, vol 80. Birkhäuser Basel. https://doi.org/10.1007/978-3-0348-7192-1_40
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DOI: https://doi.org/10.1007/978-3-0348-7192-1_40
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