On pexider additive functional equations

Authors

  • Tamás Glavosits University of Miskolc
  • Zsolt Karácsony University of Miskolc

DOI:

https://doi.org/10.35925/j.multi.2023.3.27

Keywords:

Additive functions, additive functional equations, Pexider additív functional equations, restricted Pexider additive fumnctional equations, Archimedean ordered Abelian groups, ordered dense groups, general solution of functional equations, discrete sets

Abstract

Let Y(+) egy Abelian group, D in Z2 ( Z(+,≤) denotes the ordered group of the integers).
Dx:={uϵZ | exists vϵ X; (u,v)ϵ D}, Dy:={vϵZ | exists uϵ X; (u,v)ϵ D}, Dx+y:={zϵZ | exists (u,v)ϵ D; z=u+v}.The aim of the article is to find sets D in Z2 that the general solution of the functional equation f(x+y) = g(x) + h(y) ((x,y ϵ D) with unknown functions f, g and h is in the form of f(u)=a(u)+C1+C2 (uϵDx+y), g(v)=a(v)+C1 (vϵDx); h(z)=a(z)+C2 (zϵDy) where a is an additive function, C1, C2 ϵ Y are constants).

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Published

2023-12-21