- Tytuł:
- Φ- α(⋅)-K-monotone multifunctions with values in ordered Banach space with increasing norm
- Autorzy:
- Rolewicz, S.
- Powiązania:
- https://bibliotekanauki.pl/articles/206769.pdf
- Data publikacji:
- 2013
- Wydawca:
- Polska Akademia Nauk. Instytut Badań Systemowych PAN
- Tematy:
-
vector valued functions
normal cone
cone with bounded basis
Φ-α(⋅)-K-subgradi-ents
increasing norm
Φ-α(⋅)-k-subdifferential Fréchet Φ-differentiability - Opis:
- Let (X, d) be a metric space. Let Y be an ordered Banach space with increasing norm. Let Φ be a separable linear family (a class) of Lipschitz functions defined on X and with values in Y . Let α(⋅) be a nondecreasing function mapping the interwal [0,+∞) into itself such that limt↓0 α(t) / t = 0. We say that a multifunction mapping X into Φ is Φ -α(⋅)-K-monotone if for all k in the interior of K, k ∈ Int K, there is a constant Ck > 0 such that for all φx ∈Γ (x),φy ∈Γ (y) we have φx(x) + φy(y) − φx(y) − φy(x) ≥K −Ckα(d(x, y))k.It is shown in the paper that under certain conditions on each Φ - Φα(⋅)-K-monotone multifunction is single-valued and continuous on a dense G δ-set..
- Źródło:
-
Control and Cybernetics; 2013, 42, 4; 793-803
0324-8569 - Pojawia się w:
- Control and Cybernetics
- Dostawca treści:
- Biblioteka Nauki
Artykuł