Convex-like inequality, homogeneity, subadditivity, and a characterization of Lp-norm
Janusz Matkowski ; Marek Pycia
Annales Polonici Mathematici, Tome 62 (1995), p. 221-230 / Harvested from The Polish Digital Mathematics Library
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Let a and b be fixed real numbers such that 0 < mina,b < 1 < a + b. We prove that every function f:(0,∞) → ℝ satisfying f(as + bt) ≤ af(s) + bf(t), s,t > 0, and such that limsupt→0+f(t)≤0 must be of the form f(t) = f(1)t, t > 0. This improves an earlier result in [5] where, in particular, f is assumed to be nonnegative. Some generalizations for functions defined on cones in linear spaces are given. We apply these results to give a new characterization of the Lp-norm.

Publié le : 1995-01-01
EUDML-ID : urn:eudml:doc:262515 
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Janusz Matkowski; Marek Pycia. Convex-like inequality, homogeneity, subadditivity, and a characterization of $L^p$-norm. Annales Polonici Mathematici, Tome 62 (1995) pp. 221-230. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-apmv60z3p221bwm/

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