Local stability of the additive functional equation and its applications
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.
scientific article; zbMATH DE number 1883655