- Tytuł:
- Convex-like inequality, homogeneity, subadditivity, and a characterization of $L^p$-norm
- Autorzy:
-
Matkowski, Janusz
Pycia, Marek - Powiązania:
- https://bibliotekanauki.pl/articles/1311612.pdf
- Data publikacji:
- 1995
- Wydawca:
- Polska Akademia Nauk. Instytut Matematyczny PAN
- Tematy:
-
functional inequality
subadditive functions
homogeneous functions
Banach functionals
convex functions
linear space
cones
measure space
integrable step functions
$L^p$-norm
Minkowski's inequality - Opis:
- Let a and b be fixed real numbers such that 0 < min{a,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 $limsup_{t → 0+} f(t) ≤ 0$ 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 $L^p$-norm.
- Źródło:
-
Annales Polonici Mathematici; 1994-1995, 60, 3; 221-230
0066-2216 - Pojawia się w:
- Annales Polonici Mathematici
- Dostawca treści:
- Biblioteka Nauki
Artykuł