Approximately additive mappings in non-Archimedean normed spaces
Bull. Korean Math. Soc. 2009 Vol. 46, No. 2, 387-400
https://doi.org/10.4134/BKMS.2009.46.2.387
Printed March 1, 2009
Alireza Kamel Mirmostafaee
Ferdowsi University of Mashhad
Abstract : 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.
Keywords : Hyers-Ulam-Rassias stability, Cauchy equation, Jensen equation, Jordan-von Neumann-type Jensen inequality
MSC numbers : Primary 39B82, 39B22, 46S10; Secondary 39B62
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