On an Asymptotic Behavior of Exponential Functional Equation.

The stability problems of the exponential (functional) equation on a restricted domain will be investigated, and the results will be applied to the study of an asymptotic property of that equation. More precisely, the following asymptotic property is proved: Let X be a real (or complex) normed space. A mapping f : X → ℂ is exponential if and only if f( x + y) – f( x) f( y) → 0 as ‖ x‖ + ‖ y‖ → ∞ under some suitable conditions. [ABSTRACT FROM AUTHOR]