- Tytuł:
- Some remarks on the space of differences of sublinear functions
- Autorzy:
-
Bartels, Sven
Pallaschke, Diethard - Powiązania:
- https://bibliotekanauki.pl/articles/1340588.pdf
- Data publikacji:
- 1994
- Wydawca:
- Polska Akademia Nauk. Instytut Matematyczny PAN
- Tematy:
-
upper convex approximation
sublinear function
Fenchel conjugation
quasidifferentiable function - Opis:
- Two properties concerning the space of differences of sublinear functions D(X) for a real Banach space X are proved. First, we show that for a real separable Banach space (X,‖·‖) there exists a countable family of seminorms such that D(X) becomes a Fréchet space. For X = ℝ^n this construction yields a norm such that D(ℝ^n) becomes a Banach space. Furthermore, we show that for a real Banach space with a smooth dual every sublinear Lipschitzian function can be expressed by the Fenchel conjugate of the farthest point mapping to its subdifferential at the origin. This leads to a simple family of sublinear functions which contains an exhaustive family of upper convex approximations for any quasidifferentiable function.
- Źródło:
-
Applicationes Mathematicae; 1993-1995, 22, 3; 419-426
1233-7234 - Pojawia się w:
- Applicationes Mathematicae
- Dostawca treści:
- Biblioteka Nauki