A special class of functional equations

Rok, strany: 2018, 397 - 404

We obtain in terms of additive and multi-additive functions the solutions $f,h:S\rightarrow H$ of the functional equation \begin{equation*} \underset{λ \in Φ}{∑}f(x+λ y+a_λ)=Nf(x)+h(y),  x,y\in S, \end{equation*} where $(S,+)$ is an abelian monoid, $Φ$ is a finite group of automorphisms of $S$, $N=\vert Φ \vert$ designates the number of its elements, $\{a_λ, λ \in Φ \}$ are arbitrary elements of $S$ and $(H,+)$ is an abelian group. In addition, some applications are given. This equation provides a joint generalization of many functional equations such as Cauchy's, Jensen's,

ISO 690:

Charifi, A., Łukasik, R., Zeglami, D. 2018. A special class of functional equations. In Mathematica Slovaca, vol. 68, no.2, pp. 397-404. 0139-9918. DOI: https://doi.org/10.1515/ms-2017-0110

APA:

Charifi, A., Łukasik, R., Zeglami, D. (2018). A special class of functional equations. Mathematica Slovaca, 68(2), 397-404. 0139-9918. DOI: https://doi.org/10.1515/ms-2017-0110