Approximately additive function

Summary

An approximately additive function is a map $f$ from an abelian group to a normed space. The norm of its defect $f(x + y) - f(x) - f(y)$ is at most a fixed $\delta$. It is an additive function up to a uniform error. Hyers' theorem says that an approximately additive map from a normed space to a Banach space lies within $\delta$ of a unique additive map. Such maps are also called $\delta$-additive maps.