Functions of bounded variation arising from a generalized two-normed space

Abstract

The first formal development of functions with bounded variation in normed spaces is attributed to Chistyakov [5], and was later extended to the context of 2-normed spaces 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 of functions of bounded 2-variation within the context of generalized two-normed spaces are explored in detail (see Theorems 4.4, 4.12, 4.13). Additionally, it is shown that a function of bounded variation defined on a semi-normed space can generate a function of bounded 2-variation in the context of generalized two-normed spaces (Proposition 4.10).