Abstract
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.
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