The aim of this note is to give a type of characterization of Banach spaces in terms of the stability of functional equations. More precisely, we prove that a normed space X is complete if there exists a functional equation of the type sum_{i=1}^{n}a_if( vph_i(x_1, ldots,x_k))=0 qquad(x_1, ldots,x_k in D) with given real numbers a_1, ldots,a_n$, given mappings vph_1 ldots, vph_n colon D^k to D and unknown function f colon D to X , which has a Hyers--Ulam stability property on an infinite subset D of the integers.

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