On Ulam's Type Stability of the Cauchy Additive Equation

Abstract EN

We prove a general result on Ulam's type stability of the functional equation f x + y = f x + f y , 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.