- Tytuł:
- Generalized approximate midconvexity
- Autorzy:
- Tabor, J.
- Powiązania:
- https://bibliotekanauki.pl/articles/969650.pdf
- Data publikacji:
- 2009
- Wydawca:
- Polska Akademia Nauk. Instytut Badań Systemowych PAN
- Tematy:
-
approximately midconvex function
convexity
paraconvexity
semiconcavity - Opis:
- Let X be a normed space and V ⊂ X a convex set with nonempty interior. Let α : [0, ∞) → [0, ∞) be a given nondecreasing function. A function ƒ : V → R is α(⋅)-midconvex if ƒ [wzór]. In this paper we study α(⋅)-midconvex functions. Using a version of Bernstein-Doetsch theorem we prove that if ƒ is α(⋅)-midconvex and locally bounded from above at every point then ƒ(rx + (1 - r)y) ≤ rƒ(x) + (1 - r)ƒ(y) + Pα(r, ¦¦x - y¦¦) for x,y ∈ V and r ∈ [0,1], where Pα : [0,1] x [0,∞) → [0,∞) is a specific function dependent on α. We obtain three different estimations of Pα. This enables us to generalize some results concerning paraconvex and semiconcave functions.
- Źródło:
-
Control and Cybernetics; 2009, 38, 3; 655-669
0324-8569 - Pojawia się w:
- Control and Cybernetics
- Dostawca treści:
- Biblioteka Nauki
Artykuł