Φ-α(⋅)-K-monotone Multifunctions with Values in Ordered Banach Space with Increasing Norm

• Autorzy: Stefan Rolewicz
• 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 C_k > 0 such that for all φ_x ∈ Γ(x), φ_y ∈ Γ(y) we have
     φ_x(x) + φ_y(y) - φ_x(y) - φ_y(x) ≥ K -C_kα(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

Statistic process control (SPC); Functional analysis

PL

Statystyczne Sterowanie Procesem; Analiza funkcjonalna

• Czasopismo: Control and Cybernetics
• Rocznik: 2013
• Tom: 42
• Numer: nr 4
• Strony: 793--803

Twórcy

autor

Stefan Rolewicz

• Institute of Mathematics of the Polish Academy of Sciences

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