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On the stability of functional equations on a restricted domain and a related topic. (English) Zbl 0844.39006
Rassias, Themistocles M. (ed.) et al., Stability of mappings of Hyers-Ulam type. Palm Harbor, FL: Hadronic Press. 141-151 (1994).
Summary: An asymptotic condition characterizing additive functionals \(f : X \to \mathbb{R}\) on a real normed space \(X = (X, |\cdot |)\) is deduced from the stability (in the sense of D. H. Hyers and S. M. Ulam) of the functional equation \(|f(x + y) |= |f(x) + f(y) |\) on a suitable “restricted domain” in \(X \times X\).
For the entire collection see [Zbl 0835.00001].

39B22 Functional equations for real functions
39B52 Functional equations for functions with more general domains and/or ranges