Uniformly bounded superposition operators in the space of second bounded variation functions in the sense of Shiba (Publicaciones en Ciencias y Tecnología, 2016)
In this paper we introduce the notion of “function of second bounded variation” in the sense of Shiba, and we show that if a superposition operator applies the space of all such functions on itself and it is uniformly bounded, then its generating function satisfies a Matkowski condition.
Keywords: Bounded variation; superposition operator; Waterman-Shiba