- Tytuł:
- Baire measurability of \((M,N)\)-Wright convex functions
- Autorzy:
- Lewicki, Michał
- Powiązania:
- https://bibliotekanauki.pl/articles/746698.pdf
- Data publikacji:
- 2008
- Wydawca:
- Polskie Towarzystwo Matematyczne
- Tematy:
-
Wright convexity
functional inequalities
regularity property
Baire measurable functions
continuous functions - Opis:
- Let \(I \subset \mathbb{R}\) be an open interval and \(M, N \colon I^2 \to I\) be means on \(I\). Let \(\varphi\colon I \to \mathbb{R}\) be a solution of the functional equation \[ \varphi(M (x, y)) + \varphi(N (x, y)) = \varphi(x) + \varphi(y),\quad x, y \in I \] We give sufficient conditions on \(M, N\) and the function \(\varphi\) such that for every Baire measurable solution \(f \colon I \to \mathbb{R}\) of the functional inequality \[ f (M (x, y)) + f (N (x, y)) \leq f (x) + f (y),\quad x, y \in I, \] the function \(f \circ \varphi^{-1} \colon \varphi(I) \to \mathbb{R}\) is convex.
- Źródło:
-
Commentationes Mathematicae; 2008, 48, 1
0373-8299 - Pojawia się w:
- Commentationes Mathematicae
- Dostawca treści:
- Biblioteka Nauki
Artykuł