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3 Scientific Issues of Jan Długosz University in Częstochowa. Mathematics

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Uniformly continuous composition operator in the space of functions of two variables of Bounded ɸ-variation in the sense of Schramm

Aziz W., Ereú T., Merentes N., Sanchez J. L., Wróbel M.

Scientific Issues of Jan Długosz University in Częstochowa. Mathematics

2012

Vol. 17

7-16

We prove in this paper that if the composition operator H, generated by a function h : I b a x C(Iba) Y , maps ɸBV (Iba ,C) into ɸ2 BV (Iba , Y ) and is uniformly continuous, then the left-left regularization h* of h is an affine function with respect to the third variable.

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

Ereú T., Merentes N., Sanchez J. L., Wróbel M.

Scientific Issues of Jan Długosz University in Częstochowa. Mathematics

2012

Vol. 17

37-47

We prove that, under some general assumptions, the one-sided regularizations of the generator of any uniformly bounded set-valued composition operator, acting in the spaces of functions of bounded variation in the sense of Schramm with nonempty bounded closed and convex values is an aﬃne function. As a special case, we obtain an earlier result ([15]).

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

Ereú T., Sánchez J. L., Merentes N., Wróbel M.

Scientific Issues of Jan Długosz University in Częstochowa. Mathematics

2011

Vol. 16

23--32

We show that the one-sided regularizations of the generator of any uniformly continuous set-valued Nemytskij operator, acting between the spaces of functions of bounded variation in the sense of Schramm, is an affine function. Results along these lines extend the study [1].