<abstract xmlns="http://www.w3.org/1999/xhtml"><p>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 <italic>p</italic>-adic valuation. Moreover a result by Z<sc>ygfryd</sc> K<sc>ominek</sc> ([5]) on the stability of the Pexider equation is formulated and proved in the context of Banach spaces over the field of <italic>p</italic>-adic numbers.</p></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.

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

Annales Mathematicae Silesianae

This work is licensed under the Creative Commons Attribution 4.0 International License.

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...

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

Published Online: May 08, 2020

Page range: 151 - 163

Received: Nov 05, 2019

Accepted: Feb 29, 2020

DOI: https://doi.org/10.2478/amsil-2020-0002

Keywords
Cauchy equation, Hyers-Ulam stability, -adic functional analysis

© 2020 Jens Schwaiger, published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

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

Published Online: May 08, 2020

Page range: 151 - 163

Received: Nov 05, 2019

Accepted: Feb 29, 2020

DOI: https://doi.org/10.2478/amsil-2020-0002

KeywordsCauchy equation, Hyers-Ulam stability, -adic functional analysis

© 2020 Jens Schwaiger, published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Keywords
Cauchy equation, Hyers-Ulam stability, -adic functional analysis