## 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
Full Text: