| On an Asymptotic Behavior of Exponential Functional Equation |
| |
| 作者姓名： | Soon Mo JUNG |
| |
| 作者单位： | Mathematics Section, College of Science and Technology, Hong-Ik University, 339-701 Chochiwon, Korea |
| |
| 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.
|
| 关 键 词： | 指数方程 稳定性 限制域 渐进线 映射 |
| 收稿时间： | 2003-10-23 |
| 修稿时间： | 2003-10-232004-05-31 |
On an Asymptotic Behavior of Exponential Functional Equation |
| |
| Soon Mo Jung.On an Asymptotic Behavior of Exponential Functional Equation[J].Acta Mathematica Sinica,2006,22(2):583-586. |
| |
| Authors: | Soon Mo Jung |
| |
| Institution: | Soon-Mo;JUNG |
| |
| 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. |
| |
| Keywords: | Exponential equation Stability Superstability |
| 本文献已被 维普 SpringerLink 等数据库收录！ |
