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 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. © 2014 Janusz Brzdȩk.