## HYERS-ULAM STABILITY FOR A SPECIAL CLASS OF FUNCTIONAL EQUATIONS

### Abstract

In this paper, we investigate the stability in the sense of Hyers-Ulam for aclass of the following type functional equations:$$\sum_{\lambda \in \Phi}{f(x+\lambda y+a_{\lambda})}=Nf(x)+h(y),\ x,y\in S$$where $\mathbb{K}$ is a complete valued field of characteristic zero, $F$ isa complete normed space (Archimedean or ultrametric) over$\mathbb{K}$, $(S,+)$ is an abelian monoid, $f,h\colon S\to F$,$\Phi$ is a finite automorphism group of $S$, $N$ is thecardinality of $\Phi$ and $a_{\lambda}\in S$, $\lambda \in \Phi$

Topics: Hyers-Ulam stability, Archimedean, ultarmetric, functional equation, Primary 20B25; Secondary 39B82
Publisher: 'University of Nis'
Year: 2018
DOI identifier: 10.22190/FUMI1705715C
OAI identifier: oai:casopisi.junis.ni.ac.rs:article/2784

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