HYERS-ULAM STABILITY FOR A SPECIAL CLASS OF FUNCTIONAL EQUATIONS

Facta Universitatis. Series Mathematics and Informatics

Ahmed Charifi¹  Muaad Almahalebi¹  Radosław Łukasik² 

[1] Ibn Tofail University;University of Silesia ul. Bankowa

关键词: Hyers-Ulam stability;    Archimedean;    ultarmetric;    functional equation;   

DOI  :  10.22190/FUMI1705715C

学科分类：社会科学、人文和艺术（综合）

来源: Univerzitet u Nishu / University of Nis

【 摘 要 】

In this paper, we investigate the stability in the sense of Hyers-Ulam for a class of the following type functional equations:$$\sum_{\lambda \in \Phi}{f(x+\lambda y+a_{\lambda})}=Nf(x)+h(y),\ x,y\in S$$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, $f,h\colon S\to F$, $\Phi$ is a finite automorphism group of $S$, $N$ is the cardinality of $\Phi$ and $a_{\lambda}\in S$, $\lambda \in \Phi$.

【 授权许可】

Unknown