Skip to main content
Log in

The Stability of Jensen’s Equation on Amenable Locally Compact Groups

  • Published:
Results in Mathematics Aims and scope Submit manuscript

Abstract

The stability of Jensen’s equation on amenable locally compact groups is proved in this note.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Z. Boros, Zs. Páles and P. Volkmann, On stability for the Jensen equation on intervals, Aequationes Math. 60 (2000), 291–297.

    Article  MathSciNet  MATH  Google Scholar 

  2. G. L. Forti, The stability of homomorphisms and amenability, with applications to functional equations, Abh. Math. Sem. Univ. Hamburg 57 (1987), 215–226.

    Article  MathSciNet  MATH  Google Scholar 

  3. G. L. Forti, Hyers-Ulam stability of functional equations in several variables, Aequationes, Math. 50 (1995), 143–190.

    MathSciNet  MATH  Google Scholar 

  4. Z. Gajda, Local stability of the functional equation characterizing polynomial functions, Ann. Polon. Math. 52 (1990), 119–137.

    MathSciNet  MATH  Google Scholar 

  5. Z. Gajda, Invariant means and representations of semigroups in the theory of functional equations, Prace Nauk. Uniw. Ślask Katowice, 1992.

  6. D. H. Hyers, G. Isac, Th. M. Rassias, Stability of Functional Equations in Several Variables, Birkhauser, Basel, 1995.

    Google Scholar 

  7. S.-M. Jung, Hyers-Ulam-Rassias stability of Jensen’s equation and its application, Proc. Amer. Math. Soc. 126 (1998), 3137–3143.

    Article  MathSciNet  MATH  Google Scholar 

  8. Z. Kominek, On a local stability of the Jensen functional equation, Demonstratio Math. 22 (1989), 499–507.

    MathSciNet  MATH  Google Scholar 

  9. C. T. Ng, Jensen’s functional equation on groups, Aequationes Math. 39 (1990), 85–99.

    Article  MathSciNet  MATH  Google Scholar 

  10. A. T. Paterson, Amenability, American Mathematical Society, 1988.

  11. A. Simon Et P. Volkmann, Perturbations de fonctions additive, Ann. Math. Silesianae 11 (1997), 21–27.

    Google Scholar 

  12. L. Székelyhidi, Fréche’s equation and Hyers theorem on noncommutative semigroups, Ann. Polon. Math. 48 (1988), 183–189.

    MathSciNet  MATH  Google Scholar 

  13. J. Tabor and J. Tabor, Remarks 15, Report of Meeting: 34th International Symposium on Functional Equations, Aequationes Math. 53 (1997), 192–193.

    Google Scholar 

  14. D. L. Yang, The stability of the quadratic functional equation on amenable groups, J. Math. Anal. Appl. 291 (2004), 666–672.

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Dilian Yang.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Yang, D. The Stability of Jensen’s Equation on Amenable Locally Compact Groups. Results. Math. 46, 381–388 (2004). https://doi.org/10.1007/BF03322890

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF03322890

2000 Mathematics Subject Classification

Key words and phrases

Navigation