asymptotic

F. Skof investigated an interesting asymptotic property of the additive functions (see Theorem 2.34). In fact, she proved that a function f : E₁ → E₂ is additive if and only if ‖f(x + y) − f(x) − f(y)‖ → 0 as ‖x‖ + ‖y‖ → ∞, where E₁ is a normed space and E₂ is a Banach space.

The asymptotic behavior of a function