Abstract
We present a result concerning the hyperstability of the general linear equation. Namely, we show that a function satisfying the equation approximately must be actually a solution to it.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Aoki T.: On the stability of the linear transformation in Banach spaces. J. Math. Soc. Jpn. 2, 64–66 (1950)
Badea C.: The general linear equation in stable. Nonlinear Funct. Anal. Appl. 10, 155–164 (2005)
Bourgin D.G.: Approximately isometric and multiplicative transformations on continuous function rings. Duke Math. J. 16, 385–397 (1949)
Brzdȩk, J.: Hyperstability of the Cauchy equation on restricted domains. Acta Math. Hungar. doi:10.1007/s10474-013-0302-3
Brzdȩk J., Chudziak J., Páles Zs.: A fixed point approach to stability of functional equations. Nonlinear Anal. 74, 6728–6732 (2011)
Brzdȩk J., Pietrzyk A.: A note on stability of the general linear equation. Aequationes Math. 75, 267–270 (2008)
Gajda Z.: On stability of additive mappings. Int. J. Math. Math. Sci. 14, 431–434 (1991)
Gǎvruţa P.: A generalization of the Hyers-Ulam-Rassias stability of approximately additive mapping. J. Math. Anal. Appl. 184, 431–436 (1994)
Hyers D.H.: On the stability of the linear functional equation. Proc. Natl. Acad. Sci. USA 27, 222–224 (1941)
Hyers D.H., Isac G., Rassias Th.M.: Stability of Functional Equations in Several Variables. Birkhäuser, Berlin (1998)
Jung S.M.: Hyers-Ulam stability of functional equations in mathematical analysis. Hadronic Press, Palm Harbor (2001)
Kuczma M.: An introduction to the theory of functional equation and inequalities. PWN, Warszawa (1985)
Maksa Gy., Páles Zs.: Hyperstability of a class of linear functional equations. Acta Math. Acad. Paedag. Nyìregyháziensis 17, 107–112 (2001)
Popa D.: Hyers-Ulam-Rassias stability of the general linear equation. Nonlinear Funct. Anal Appl. 7, 581–588 (2002)
Rassias Th.M.: On the stability of the linear mapping in Banach spaces. Proc. Am. Math. Soc. 72, 297–300 (1978)
Rassias Th.M.: On a modified Hyers-Ulam sequence. J. Math. Anal. Appl. 158, 106–113 (1991)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution License which permits any use, distribution, and reproduction in any medium, provided the original author(s) and the source are credited.
About this article
Cite this article
Piszczek, M. Remark on hyperstability of the general linear equation. Aequat. Math. 88, 163–168 (2014). https://doi.org/10.1007/s00010-013-0214-x
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00010-013-0214-x