Stability of the Cauchy equation in ordered fields (Q2714179)

The author investigates an analogue of Ulam's classical stability question on the Cauchy functional equation for functions mapping into ordered fields. Several kinds of stability of the Cauchy equation are introduced (weakly stable, stable in Ulam's sense, uniformly stable, finitely stable) and, under certain hypothesis, it is proved that the Cauchy equation is uniformly stable and finitely stable, respectively.