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Local stability of the additive functional equation and its applications. (English) Zbl 1017.39009
The Hyers-Ulam stability of the additive functional equation for a large class of unbounded domains in Banach space is proved. Loosely speaking, it is proved that if a mapping \(f\) satisfies the additivity property approximately then there exists unique approximating additive mapping for \(f\). The result is applied to investigation of the stability of Jensen’s functional equation.

MSC:
39B82 Stability, separation, extension, and related topics for functional equations
39B52 Functional equations for functions with more general domains and/or ranges
39B55 Orthogonal additivity and other conditional functional equations
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