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Hyers-Ulam-Rassias stability of Jensen's equation and its application |
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| Authors: | Soon-Mo Jung |
| Affiliation: | Mathematics Section, College of Science and Technology, Hong-Ik University, 339-800 Cochiwon, South Korea |
| 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  satisfying  is additive if and only if ![$left| 2fleft[ (x+y)/2 right] - f(x) - f(y) right| rightarrow 0$](http://www.ams.org/proc/1998-126-11/S0002-9939-98-04680-2/gif-abstract/img5.gif){kind=small} as  . |
| Keywords: | Hyers-Ulam-Rassias stability Jensen functional equation |
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