APPROXIMATELY ADDITIVE MAPPINGS IN NON-ARCHIMEDEAN NORMED SPACES

- Journal title : Bulletin of the Korean Mathematical Society
- Volume 46, Issue 2, 2009, pp.387-400
- Publisher : The Korean Mathematical Society
- DOI : 10.4134/BKMS.2009.46.2.387

Title & Authors

APPROXIMATELY ADDITIVE MAPPINGS IN NON-ARCHIMEDEAN NORMED SPACES

Mirmostafaee, Alireza Kamel;

Mirmostafaee, Alireza Kamel;

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;

Language

English

Cited by

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Hyers-Ulam Stability of Cubic Mappings in Non-Archimedean Normed Spaces,;

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