Journal of Function Spaces

Journal of Function Spaces / 2009 / Article

Open Access

Volume 7 |Article ID 802032 | 12 pages | https://doi.org/10.1155/2009/802032

The Jensen functional equation in non-Archimedean normed spaces

Academic Editor: George Isac
Received01 Oct 2007

Abstract

We investigate the Hyers–Ulam–Rassias stability of the Jensen functional equation in non-Archimedean normed spaces and study its asymptotic behavior in two directions: bounded and unbounded Jensen differences. In particular, we show that a mapping f between non-Archimedean spaces with f(0)=0 is additive if and only if f(x+y2)f(x)+f(y)20 as max {x,y}.

Copyright © 2009 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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