MR3058477 Reviewed Ereú, Thomás; Sánchez, José L.; Merentes, Nelson; Wróbel, Małgorzata Uniformly continuous set-valued composition operators in the spaces of functions of bounded variation in the sense of Schramm. Pr. Nauk. Akad. Jana Długosza Częst. Mat. 16 (2011), 23–32. ISBN: 978-83-7455-209-7

In this paper it is established a property of a composition operator between spaces of functions of bounded variation in the sense of Schramm. Let X and Y be two real normed spaces, C a convex cone in X and I a closed bounded interval of the real line. Moreover let cc(Y) be the family of all non-empty closed convex and compact subsets of Y. The authors study the Nemytskij (composition) operator (HF)(t)=h(t,F(t)), where F: I \rightarrow C and h: I\times C \rightarrow cc(Y) is a given set-valued function. They show that if the Nemytskij operator $H$ is uniformly continuous and maps the space \Phi BV (I;C) of functions (from I to C) of bounded \Phi-variation in the sense of Schramm into the space $BS_{\Psi}(I; cc(Y))$ of set-valued functions (from I to cc(Y)) of bounded \Psi-variation in the sense of Schramm, then the one-sided regularizations h^- and h^+ of h with respect the first variable are affine with respect to the second variable. Reviewed by ( L. Di Piazza)