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Hyers-Ulam-Rassias stability of Jensen's equation and its application

Author: Soon-Mo Jung
Journal: Proc. Amer. Math. Soc. 126 (1998), 3137-3143
MSC (1991): Primary 39B72
MathSciNet review: 1476142
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Abstract: The Hyers-Ulam-Rassias stability for the Jensen functional equation is investigated, and the result is applied to the study of an asymptotic behavior of the additive mappings; more precisely, the following asymptotic property shall be proved: Let $X$ and $Y$ be a real normed space and a real Banach space, respectively. A mapping $f: X \rightarrow Y$ satisfying $f(0)=0$ is additive if and only if $\left\| 2f\left[ (x+y)/2 \right] - f(x) - f(y) \right\| \rightarrow 0$ as $\| x \| + \| y \| \rightarrow \infty$.

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Additional Information

Soon-Mo Jung
Affiliation: Mathematics Section, College of Science and Technology, Hong-Ik University, 339-800 Cochiwon, South Korea

Keywords: Hyers-Ulam-Rassias stability, Jensen functional equation
Received by editor(s): March 19, 1997
Communicated by: Palle E. T. Jorgensen
Article copyright: © Copyright 1998 American Mathematical Society