Generalized Hyers–Ulam Stability of the Additive Functional Equation.

We will prove the generalized Hyers–Ulam stability and the hyperstability of the additive functional equation f (x 1 + y 1 , x 2 + y 2 , ... , x n + y n) = f (x 1 , x 2 , ... , x n) + f (y 1 , y 2 , ... , y n). By restricting the domain of a mapping f that satisfies the inequality condition used in the assumption part of the stability theorem, we partially generalize the results of the stability theorems of the additive function equations. [ABSTRACT FROM AUTHOR]