HYERS-ULAM STABILITY FOR A SPECIAL CLASS OF FUNCTIONAL EQUATIONS

摘要

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