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2020 | 34 (1) | 151--163
Tytuł artykułu

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

Autorzy
Warianty tytułu
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)
Rocznik
Tom
Strony
151--163
Opis fizyczny
Twórcy
  • University of Graz, Austria
Bibliografia
  • N. Bourbaki, Elements of Mathematics. Topological Vector Spaces, Chapters 1-5, Transl. from the French by H.G. Eggleston and S. Madan, Springer-Verlag, Berlin, 1987.
  • G.L. Forti, An existence and stability theorem for a class of functional equations, Stochastica 4 (1980), no. 1, 23-30.
  • G.L. Forti and J. Schwaiger, Stability of homomorphisms and completeness, C.R. Math. Rep. Acad. Sci. Canada 11 (1989), no. 6, 215-220.
  • P. Găvruţa, A generalization of the Hyers-Ulam-Rassias stability of approximately additive mappings, J. Math. Anal. Appl. 184 (1994), no. 3, 431-436.
  • Z. Kominek, On Hyers-Ulam stability of the Pexider equation, Demonstratio Math. 37 (2004), no. 2, 373-376.
  • M.S. Moslehian and Th.M. Rassias, Stability of functional equations in non-Archimedean spaces, Appl. Anal. Discrete Math. 1 (2007), no. 2, 325-334.
  • 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.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.ekon-element-000171605433

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