DOI QR코드

DOI QR Code

SUPERSTABILITY OF MULTIPLICATIVE LINEAR MAPPINGS

Anjidani, Ehsan;Ansari-Piri, Esmaeil

  • Received : 2010.03.04
  • Accepted : 2010.10.08
  • Published : 2011.04.30

Abstract

Let A and B be Banach algebras with unit. Here we prove that an approximate algebra homomorphism f : A ${\rightarrow}$ B, in the sense of Rassias, is an algebra homomorphism.

Keywords

stability of functional equation;superstability;algebra homomorphism

References

  1. R. Badora, On approximate ring homomorphisms, J. Math. Anal. Appl. 276 (2002), no. 2, 589-597. https://doi.org/10.1016/S0022-247X(02)00293-7
  2. D. G. Bourgin, Approximately isometric and multiplicative transformations on continuous function rings, Duke Math. J. 16 (1949), 385-397. https://doi.org/10.1215/S0012-7094-49-01639-7
  3. J. Brzdek and A. Pietrzyk, A note on stability of the general linear equation, Aequationes Math. 75 (2008), no. 3, 267-270. https://doi.org/10.1007/s00010-007-2894-6
  4. S. Czerwik, Stability of Functional Equations of Hyers-Ulam-Rassias Type, Hadronic Press Inc., Palm Harbor, Florida, 2003.
  5. M. Eshaghi Gordji, Stability of an additive-quadratic functional equation of two variables in F-spaces, J. Nonlinear Sci. Appl. 2 (2009), no. 4, 251-259.
  6. G. L. Forti, Comments on the core of the direct method for proving Hyers-Ulam stability of functional equations, J. Math. Anal. Appl. 295 (2004), no. 1, 127-133. https://doi.org/10.1016/j.jmaa.2004.03.011
  7. P. Gavruta, A generalization of the Hyers-Ulam-Rassias stability of approximately additive mappings, J. Math. Anal. Appl. 184 (1994), no. 3, 431-436. https://doi.org/10.1006/jmaa.1994.1211
  8. D. H. Hyers, On the stability of the linear functional equation, Proc. Nat. Acad. Sci. U.S.A. 27 (1941), 222-224. https://doi.org/10.1073/pnas.27.4.222
  9. D. H. Hyers, G. Isac, and Th. M. Rassias, Stability of Functional Equations in Several Variables, Birkhauser, Boston, 1998.
  10. A. Najati and C. Park, Stability of a generalized Euler-Lagrange type additive mapping and homomorphisms in $C^{*}$-algebras, J. Nonlinear Sci. Appl. 3 (2010), no. 2, 123-143.
  11. C. Park, On an approximate automorphism on a $C^{*}$-algebra, Proc. Amer. Math. Soc. 132 (2004), no. 6, 1739-1745. https://doi.org/10.1090/S0002-9939-03-07252-6
  12. Th. M. Rassias, On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72 (1978), no. 2, 297-300. https://doi.org/10.1090/S0002-9939-1978-0507327-1
  13. S. M. Ulam, Problems in Modern Mathematics, Science Editions, Wiley, New York, 1964.