The formulas for the representation of functions of two variables as a difference of sublinear functions

ABSTRACT

Having a function being a difference of sublinear functions defined on a plane, we present a formula for effective calculation of sublinear functions such that their difference is equal to the given one. Moreover, these newly calculated sublinear functions are minimal and as such unique-up-to-linear-summand. We also provide examples of such functions.

KEYWORDS:

• Differences of sublinear functions (ds-functions)
• minimal representation of ds-function
• support functions
• subdifferential and superdifferential

AMS CLASSIFICATIONS:

• 26B25
• 49J52
• 52A10
• 54C35

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Diethard Pallaschke  http://orcid.org/0000-0002-1812-2597