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

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- by Soon-Mo Jung
- Proc. Amer. Math. Soc.
**126**(1998), 3137-3143 - DOI: https://doi.org/10.1090/S0002-9939-98-04680-2
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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 $\| x \| + \| y \| \rightarrow \infty$.## References

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## Bibliographic Information

**Soon-Mo Jung**- Affiliation: Mathematics Section, College of Science and Technology, Hong-Ik University, 339-800 Cochiwon, South Korea
- Email: smjung@wow.hongik.ac.kr
- Received by editor(s): March 19, 1997
- Communicated by: Palle E. T. Jorgensen
- © Copyright 1998 American Mathematical Society
- Journal: Proc. Amer. Math. Soc.
**126**(1998), 3137-3143 - MSC (1991): Primary 39B72
- DOI: https://doi.org/10.1090/S0002-9939-98-04680-2
- MathSciNet review: 1476142