摘要
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.
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.
