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.


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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