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Zbl 1163.39019
Mirmostafaee, Alireza Kamel
Approximately additive mappings in non-Archimedean normed spaces.
(English)
[J] Bull. Korean Math. Soc. 46, No. 2, 387-400 (2009). ISSN 1015-8634

Author's summary: We establish a new strategy to study the Hyers-Ulam-Rassias stability of the Cauchy and Jensen equations in non-Archimedean normed spaces. We will also show that under some restrictions, every function which satisfies certain inequalities can be approximated by an additive mapping in non-Archimedean normed spaces. Some applications of our results will be exhibited. In particular, we will see that some results about stability and additive mappings in real normed spaces are not valid in non-Archimedean normed spaces.'' A recent related paper is: {\it A. K. Mirmostafaee} and {\it M. S. Moslehian} [Stability of additive mappings in non-Archimedean fuzzy normed spaces, Fuzzy Sets and Systems, 160 (11), 1643--1652 (2009)].
[Paşc Găvruţă (Timişoara)]
MSC 2000:
*39B82 Stability, separation, extension, and related topics
46S10 Functional analysis over fields (not R, C, or quaternions)
39B52 Functional equations for functions with more general domains

Keywords: Hyers-Ulam-Rassias stability; Cauchy functional equation; Jensen functional equation; Jordan-von Neumann-type Jensen inequality; non-Archimedean normed spaces; additive mapping

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