On Ulam's type stability of the Cauchy additive equation.
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.
Department of Mathematics, Pedagogical University, Podchorążych 2, 30-084 Kraków, Poland.
Janusz
J
Brzdęk
D055641:Mathematical Concepts; D015233:Models, Statistical