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In this paper we prove that if the composition operator H of generator h : Iba× C → Y (X is a real normed space, Y is a real Banach space, C is a convex cone in X and Iba⸦ R2) maps Φ1BV (Iba, C) into Φ2BV (Iba, Y) and is uniformly bounded, then the left-left regularization h* of h is an affine function in the third variable.
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]).
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].
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