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Elementary remarks on Ulam-Hyers stability of linear functional equations. (English) Zbl 1111.39026
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.

##### MSC:
 39B82 Stability, separation, extension, and related topics for functional equations 39B52 Functional equations for functions with more general domains and/or ranges
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