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http://dx.doi.org/10.4134/BKMS.2009.46.2.387

APPROXIMATELY ADDITIVE MAPPINGS IN NON-ARCHIMEDEAN NORMED SPACES  

Mirmostafaee, Alireza Kamel (DEPARTMENT OF MATHEMATICS SCHOOL OF MATHEMATICAL SCIENCES FERDOWSI UNIVERSITY)
Publication Information
Bulletin of the Korean Mathematical Society / v.46, no.2, 2009 , pp. 387-400 More about this Journal
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;
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Times Cited By Web Of Science : 5  (Related Records In Web of Science)
Times Cited By SCOPUS : 7
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