an:05124056
Zbl 1111.39026
Forti, Gian-Luigi
Elementary remarks on Ulam-Hyers stability of linear functional equations
EN
J. Math. Anal. Appl. 328, No. 1, 109-118 (2007).
0022-247X
2007
j
39B82 39B52
Hyers-Ulam stability; linear functional equation; Banach space,
The author proves the Hyers-Ulam stability of the family of linear functional equations of the form
\[
\sum_{i=1}^s b_iF\big(\sum_{k=1}^m a_{ik}x_k\big)=0,
\]
where \(F: S \to X\), \(S\) is a vector space over a field \({\mathbb K}\) of characterisitic zero, \(X\) is a complex Banach space, \(b_1, \cdots, b_s\) are nonzero complex numbers with \(\sum_{i=1}^s b_i \neq 0\), \(a_{ik}\in {\mathbb K} \quad (1 \leq i \leq s, 1 \leq k \leq m)\), \(x_k \in S \quad (1 \leq k \leq m)\). Several useful remarks and open problems are also given.
Mohammad Sal Moslehian (Mashhad)