Connections between the completion of normed spaces over non-archimedean fields and the stability of the Cauchy equation
Abstract
In [12] a close connection between stability results for the Cauchy equation and the completion of a normed space over the rationals endowed with the usual absolute value has been investigated. Here similar results are presented when the valuation of the rationals is a p-adic valuation. Moreover a result by Zygfryd Kominek ([5]) on the stability of the Pexider equation is
formulated and proved in the context of Banach spaces over the field of p-adic numbers.
Keywords
Cauchy equation; Hyers-Ulam stability; p-adic functional analysis
References
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Institute of Mathematics and Scientific Computing, University of Graz, Austria Austria
https://orcid.org/0000-0002-4142-0146
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