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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.

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

Azocar A., Guerrero J. A., Matkowski J., Merentes N.

Opuscula Mathematica

2010

Vol. 30, no. 1

53-60

We show that the one-sided regularizations of the generator of any uniformly continuous and convex compact valued composition operator, acting in the spaces of functions of bounded variation in the sense of Wiener, is an affine function.