FUNCTIONS OF BOUNDED VARIATION ARISING FROM A GENERALIZED TWO-NORMED SPACE

Abstract

The first formal development of functions with bounded variation in normedspaces is attributed to Chistyakov [5], and was later extended to the context of 2-normedspaces by Cure, Ferrer S., and Ferrer V. [6]. In this paper, we elaborate on this extension(Definition 4.5), exploring its fundamental properties. The foundational characteristics offunctions of bounded 2-variation within the context of generalized two-normed spaces areexplored in detail (see Theorems 4.4, 4.12, 4.13). Additionally, it is shown that a functionof bounded variation defined on a semi-normed space can generate a function of bounded2-variation in the context of generalized two-normed spaces (Proposition 4.10).