Proceedings of the American Mathematical Society

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ISSN 1088-6826(e) ISSN 0002-9939(p)

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

Author(s): 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 and be a real normed space and a real Banach space, respectively. A mapping $f: X \rightarrow Y$ satisfying 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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