Stability of the preservation of the equality of distance

We study the stability problem for mappings satisfying the equation f (x −y) = f (x)− f (y) . As a result we obtain the stability of functions preserving the equality of distance, that is, satisfying for all x, y,u, v the condition x −y = u −v ⇒ f (x)− f (y) = f (u) −f (v) .  2005 Elsevier Inc. All rights reserved.