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- Title
ON PEXIDER ADDITIVE FUNCTIONAL EQUATIONS.
- Authors
Glavosits, Tamás; Karácsony, Zsolt
- Abstract
Let Y(+) egy Abelian group, D ⊆ 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 ⊆ 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:Z→ Y is an additive function, C1, C2 ϵ Y are constants).
- Subjects
FUNCTIONAL equations; ABELIAN groups; ADDITIVE functions; ARCHIMEDEAN property; EXISTENCE theorems
- Publication
Multidiszciplináris Tudományok, 2023, Vol 13, Issue 3, p277
- ISSN
2062-9737
- Publication type
Article
- DOI
10.35925/j.multi.2023.3.27