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

Authors

  • Osmin Ferrer Villar 1Department of Mathematics, University of Sucre
  • Kandy Ferrer Sotelo 2Center for Basic Sciences, School of Engineering and Architecture, Pontical Bolivarian University
  • Jaffeth Cure Arenas 3Department of Applied Mathematics and Physics, Catholic University of the Most Holy Conception

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).

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Published

2025-11-29

Issue

Volume 30, Number 4, December 2025

Section

Articles