## On the stability of the Cauchy functional equation: a fixed point approach.(English)Zbl 1060.39028

The authors apply a well known fixed point theorem to the proof of Hyers-Ulam-Rassias stability of the additive Cauchy functional equation. This method is a new and attractive one in researching stability problems and seems to be applied to investigating stability phenomena of other functional equations.

### MSC:

 39B82 Stability, separation, extension, and related topics for functional equations 47H09 Contraction-type mappings, nonexpansive mappings, $$A$$-proper mappings, etc.