Φ- α(⋅)-K-monotone multifunctions with values in ordered Banach space with increasing norm

• Autorzy: Rolewicz S.
• Języki publikacji: EN

Abstrakty

EN

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 lim_t↓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..

Słowa kluczowe

EN

vector valued functions; normal cone; cone with bounded basis; Φ-α(⋅)-K-subgradi-ents; increasing norm; Φ-α(⋅)-k-subdifferential Fréchet Φ-differentiability

• Wydawca: Systems Research Institute, Polish Academy of Sciences
• Czasopismo: Control and Cybernetics
• Rocznik: 2013
• Tom: Vol. 42, no. 4
• Strony: 793--803
• Opis fizyczny: Bibliogr. 20 poz.

Twórcy

autor

Rolewicz S.

• Institute of Mathematics of the Polish Academy of Sciences Śniadeckich 8, 00-956 Warszawa, P.O.Box 21, Poland

Bibliografia

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