Skip to main content
SpringerLink
Log in

Special cases of the generalized Hosszú equation on interval

  • Published:
Aequationes mathematicae Aims and scope Submit manuscript

Abstract

In this paper we determine the general solution of some special cases of the generalized Hosszú functional equation on intervals [0,1] and (0,1).

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Aczél J.: Diamonds are not the Cauchy extensionist’s best friend. C. R. Math. Rep. Acad. Sci. Can. 5, 259–264 (1983)

    MATH  Google Scholar 

  2. Aczél, J., Dhombres, J.: Functional Equations in Several Variables. Cambridge University Press, Cambridge (1989)

  3. Blanuša D.: The functional equation f(x + y−xy) + f(xy) = f(x) + f(y). Aequationes Math. 5, 63–70 (1970)

    Article  MATH  MathSciNet  Google Scholar 

  4. Daróczy Z.: Über die Funktionalgleichung f(x + y−xy) + f(xy) = f(x) + f(y). Publ. Math. Debr. 16, 129–132 (1969)

    MATH  Google Scholar 

  5. Daróczy Z.: On the general solution of the functional equation f(x + y−xy) + f(xy) = f(x) + f(y). Aequ. Math. 6, 130–132 (1971)

    Article  MATH  Google Scholar 

  6. Daróczy Z., Losonczi L.: Über die Erweiterung der auf einer Punktmenge additiven Funktionen. Publ. Math. Debr. 14, 239– (1967)

    MATH  Google Scholar 

  7. Daróczy Z., Lajkó K., Székelyhidi L.: Functional equations on ordered fields. Publ. Math. Debr. 24, 173–179 (1977)

    MATH  Google Scholar 

  8. Davison T.M.K.: On the functional equation f(m + n−mn) + f(mn) = f(m) + f(n). Aequ. Math. 10, 206–211 (1974)

    Article  MATH  MathSciNet  Google Scholar 

  9. Davison T.M.K.: The complete solution of Hosszú’s functional equation over field. Aequ. Math. 11, 273–276 (1974)

    Article  MATH  MathSciNet  Google Scholar 

  10. Davison T.M.K., Redlin L.: Hosszú’s functional equation over rings generated by their units. Aequ. Math. 21, 121–128 (1980)

    Article  MATH  MathSciNet  Google Scholar 

  11. Fenyő I.: Über die Funktoionalgleichung f(a 0 + a 1 x + a 2 y + a 3 xy) + g(b 0 + b 1 x + b 2 y + b 3 xy) = h(x) + k(y). Acta Math. Hung. 21, 35–46 (1970)

    Article  Google Scholar 

  12. Hajdu G., Hajdu L.: Hosszú’s equation over the Gaussian and Eisenstein integers. Aequ. Math. 75, 65–74 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  13. Kuczma, M.: Introduction to the Theory of Functional Equations and Inequalities, 2nd edn. Birkhäuser Verlag AG (2008)

  14. Lajkó K.: Applications of extensions of additive functions. Aequ. Math. 11, 68–76 (1974)

    Article  MATH  Google Scholar 

  15. Lajkó K.: Remark to a paper by J. A. Baker. Aequ. Math. 19, 227–233 (1979)

    Article  MATH  Google Scholar 

  16. Lajkó K.: Generalized Hosszú functional equations. Ann. Acad. Paed. Cracoviensis, Stud. Math. I 4, 59–68 (2001)

    Google Scholar 

  17. Lajkó K., Maksa G.y., Mészáros F.: On a generalized Hosszú functional equation. Publ. Math. Debr. 74, 101–106 (2009)

    MATH  Google Scholar 

  18. Światak H.: Remarks on the functional equation f(x + y−xy) + f(xy) = f(x) + f(y). Aequ. Math. 1, 239–241 (1968)

    Article  MATH  Google Scholar 

  19. Światak H.: Remarks on the equation f(x + y−xy) + f(xy) = f(x) + f(y). Aequ. Math. 4, 250–251 (1970)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Mathematics, University of Debrecen, Debrecen, P.O. Box 12, 4010, Hungary

    Károly Lajkó & Fruzsina Mészáros

Authors
  1. Károly Lajkó
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Fruzsina Mészáros
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Fruzsina Mészáros.

Additional information

Dedicated to the 90th birthday of Professor János Aczél

This research has been supported by the Hungarian Scientific Research Fund (OTKA), Grant NK81402.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Lajkó, K., Mészáros, F. Special cases of the generalized Hosszú equation on interval. Aequat. Math. 89, 71–81 (2015). https://doi.org/10.1007/s00010-014-0285-3

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00010-014-0285-3

Mathematics Subject Classification

Keywords

Search

Navigation