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2 Journal of Applied Mathematics and Computational Mechanics

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Operators with memory in Schramm spaces

Wróbel Małgorzata

Journal of Applied Mathematics and Computational Mechanics

2023

Vol. 22, nr 3

69--80

We show that every operator with memory acting between Banach spaces CΦBV(I) of continuous functions of bounded variation in the sense of Schramm defined on a compact interval I of a real axis, is a Nemytskij composition operator with the continuous generating function. Moreover, some consequences for uniformly bounded operators with memory will be given. As a by-product, we obtain that a Banach space CΦBV(I) has the uniform Matkowski property.

Uniformly bounded set-valued composition operators in the spaces of functions of bounded variation in the sense of Wiener

Guerrero J. A., Matkowski J., Merentes N., Wróbel M.

Journal of Applied Mathematics and Computational Mechanics

2015

Vol. 14, nr 4

41--51

We show that the one-sided regularizations of the generator of any uniformly bounded set-valued Nemytskij composition operator mapping the space of bounded variation functions in the sense of Wiener into the space of bounded variation functions with closed bounded convex values (in the sense of Wiener) are affine functions.