Connections Between the Completion of Normed Spaces Over Non-Archimedean Fields and the Stability of the Cauchy Equation

Jens Schwaiger

doi:10.2478/amsil-2020-0002

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Connections Between the Completion of Normed Spaces Over Non-Archimedean Fields and the Stability of the Cauchy Equation

Annales Mathematicae Silesianae

Volume 34 (2020): Issue 1 (July 2020)

By: Jens Schwaiger

Open Access

|May 2020

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.

References

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Articles in this issue

DOI: https://doi.org/10.2478/amsil-2020-0002 | Journal eISSN: 2391-4238 | Journal ISSN: 0860-2107

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Language: English

Page range: 151 - 163

Submitted on: Nov 5, 2019

Accepted on: Feb 29, 2020

Published on: May 8, 2020

Published by: University of Silesia in Katowice, Institute of Mathematics

In partnership with: Paradigm Publishing Services

Publication frequency: 2 issues per year

Keywords:

Cauchy equation,

Hyers-Ulam stability,

-adic functional analysis

Related subjects:

Mathematics,

General mathematics

© 2020 Jens Schwaiger, published by University of Silesia in Katowice, Institute of Mathematics
This work is licensed under the Creative Commons Attribution 4.0 License.

Volume 34 (2020): Issue 1 (July 2020)