Bounded variation of functions defined on a convex and compact set in the plane

Abstract

In this paper, the variation of functions has been defined, whose domain is a convex and compact set in the plane. Furthermore, in addition to presenting properties that satisfy this variation, the vector space formed by functions with finite variation is studied, demonstrating that it is a Banach space and its elements can be expressed as the difference of non-decreasing functions.

2020 Mathematics Subject Classification:

• 26A45
• 26B30

Keywords and Phrases:

• Bounded variation
• compact set

Disclosure statement

The authors declare that they have no conflict of interest related to this research, either by authorship or publication. They also declare that they have not received specific funding from any source, whether commercial, public, or non-profit organizations.