On Nemytskij operator of substitution in the C1 space of set-valued functions

• Autorzy: Ludew J.
• Języki publikacji: EN

Abstrakty

EN

We consider the Nemytskij operator, i. e., the operator of substitution, defined by (N[...]x) := G(x,<[...](x)), where G is a given multifunction. It is shown that N maps C1 (I, C), the space of all continuously differentiable functions on the interval I with values in a cone C in a Banach space, into C1 (I, cc(Z)), the space of all continuously differentiable set-functions on I with compact and convex values in a Banach space Z and N fulfils the Lipschitz condition if and only if the generator G is of the form G(x,y)=A(x,y) + B(x) where A(x, •) is continuous, linear function, A(.,y) and B are continuously differentiable and the function x— > A(x, •) is Lipschitzian.

Słowa kluczowe

EN

Nemytskij operator; C1 space; Jensen equation; set-valued functions

PL

operator Nemytskija; przestrzeń C1; równanie Jensena; przestrzeń Banacha

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2008
• Tom: Vol. 41, nr 2
• Strony: 403--414
• Opis fizyczny: Bibliogr. 10 poz.

Twórcy

autor

Ludew J.

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

Bibliografia

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