On Nemytskij operator in the space of absolutely continuous set-valued functions

• Autorzy: Ludew J. J.
• Języki publikacji: EN

Abstrakty

EN

We consider the Nemytskij operator, defined by (Nφ)(x) ? G(x, φ(x)), where G is a given set-valued function. It is shown that if N maps AC(I, C), the space of all absolutely continuous functions on the interval I ? [0, 1] with values in a cone C in a reflexive Banach space, into AC(I, K), the space of all absolutely continuous set-valued functions on I with values in the set K, consisting of all compact intervals (including degenerate ones) on the real line R, and N is uniformly continuous, then the generator G is of the form G(x, y) = A(x)(y) + B(x), where the function A(x) is additive and uniformly continuous for every x ∈ I and, moreover, the functions x ? A(x)(y) and B are absolutely continuous. Moreover, a condition, under which the Nemytskij operator maps the space AC(I, C) into AC(I, K) and is Lipschitzian, is given.

Słowa kluczowe

EN

Nemytskij operator; absolutely continuous functions; set-valued functions; Jensen equation

PL

operator Nemytskija; funkcja absolutnie ciągła; zbiór wartości funkcji; równanie Jensena

• Wydawca: De Gruyter
• Czasopismo: Journal of Applied Analysis
• Rocznik: 2011
• Tom: Vol. 17, nr 2
• Strony: 277--290
• Opis fizyczny: Bibliogr. 21 poz.

Twórcy

autor

Ludew J. J.

• Institute of Mathematics, Silesian University of Technology, ul. Kaszubska 23,44-100 Gliwice, Poland,

Bibliografia

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