非阿基米德域上赋范空间的完备性与Cauchy方程稳定性的联系

IF 0.4 Q4 MATHEMATICS

Annales Mathematicae Silesianae Pub Date : 2020-05-08 DOI:10.2478/amsil-2020-0002

J. Schwaiger

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引用次数: 1

摘要

摘要在[12]中，研究了柯西方程的稳定性结果与赋有通常绝对值的有理数上赋范空间的完备性之间的密切联系。当有理数的估值是p-adic估值时，这里给出了类似的结果。此外，Zygfry-Kominek（[5]）关于Pexider方程稳定性的一个结果在p-adic数域上的Banach空间中得到了公式化和证明。

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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.

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来源期刊

Annales Mathematicae Silesianae Mathematics-Mathematics (all)

CiteScore

0.60

自引率

25.00%

发文量

审稿时长

27 weeks