On Ulam's Type Stability of the Cauchy Additive Equation

Abstract

We prove a general result on Ulam's type stability of the functional equation fx+y=fx+fy, in the class of functions mapping a commutative group into a commutative group. As a consequence, we deduce from it some hyperstability outcomes. Moreover, we also show how to use that result to improve some earlier stability estimations given by Isaac and Rassias.