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

• Autorzy: Jens Schwaiger
• Języki publikacji: EN

Abstrakty

EN

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. (original abstract)

Słowa kluczowe

EN

Mathematics; Differential equations; Functional analysis; Mathematical functions

PL

Matematyka; Równania różniczkowe; Analiza funkcjonalna; Funkcje matematyczne

• Czasopismo: Annales Mathematicae Silesianae
• Rocznik: 2020
• Tom: 34 (1)
• Strony: 151--163

Twórcy

autor

Jens Schwaiger

• University of Graz, Austria

Bibliografia

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• A. Najati and Y.J. Cho, Generalized Hyers-Ulam stability of the Pexiderized Cauchy functional equation in non-Archimedean spaces, Fixed Point Theory Appl. 2011, Art. ID 309026, 11 pp.
• C. Perez-Garcia and W.H. Schikhof, Locally Convex Spaces over Non-Archimedean Valued Fields, Vol. 119, Cambridge University Press, Cambridge, 2010.
• W.H. Schikhof, Ultrametric Calculus. An Introduction to p-adic Analysis. Paperback reprint of the 1984 original, Vol. 4, Cambridge University Press, Cambridge, 2006.
• J. Schwaiger, Remark on Hyers's stability theorem, in: R. Ger, Report of Meeting: The Twenty-fifth International Symposium on Functional Equations, Aequationes Math. 35 (1988), no. 1, 82-124,
• J. Schwaiger, Functional equations for homogeneous polynomials arising from multilinear mappings and their stability, Ann. Math. Sil. 8 (1994), 157-171.
• J. Schwaiger, On the construction of the field of reals by means of functional equations and their stability and related topics, in: J. Brzdęk et al. (eds.), Developments in Functional Equations and Related Topics, Springer, Cham, 2017, pp. 275-295.

Identyfikatory

DOI

10.2478/amsil-2020-0002