Abstract. In this paper we consider the Nemytskii operator

Abstract

(t) = h(t, f(t)), generated by a given set–valued function h is considered. It is shown that if H is globally Lipschitzian and maps the space of functions of bounded p-variation (with respect to a weight function α) into the space of set-valued functions of bounded q-variation (with respect to α) 1 < q < p, then H is of the form ( Hϕ) (t) = A(t)ϕ(t) + B(t). On the other hand, if 1 < p < q, then H is constant. It generalizes many earlier results of this type due to Chistyakov, Matkowski, Merentes-Nikodem, Merentes-Rivas, Smajdor-Smajdor and Zawadzka. Key words: variation in the sense of Riesz, set-valued functions