On pexider additive functional equations
DOI:
https://doi.org/10.35925/j.multi.2023.3.27Keywords:
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 setsAbstract
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
