Skip to main content

Approximate solutions of the generalized Gołąb-Schinzel equation

Abstract

Motivated by the problem of R. Ger, we show that the generalized Gołąb-Schinzel equation is superstable in the class of functions hemicontinuous at the origin. As a consequence, we obtain the form of approximate solutions of that equation.

[1234567891011121314]

References

  1. 1.

    Aczél J, Dhombres J: Functional Equations in Several Variables, Encyclopedia of Mathematics and Its Applications. Volume 31. Cambridge University Press, Cambridge; 1989:xiv+462.

    Google Scholar 

  2. 2.

    Brillouët-Belluot N: On some functional equations of Gołąb-Schinzel type. Aequationes Mathematicae 1991,42(2–3):239–270.

    MathSciNet  Article  MATH  Google Scholar 

  3. 3.

    Brillouët-Belluot N, Dhombres J: Équations fonctionnelles et recherche de sous-groupes. Aequationes Mathematicae 1986,31(2–3):253–293.

    MathSciNet  Article  MATH  Google Scholar 

  4. 4.

    Brzdęk J: Subgroups of the groupand a generalization of the Gołąb-Schinzel functional equation. Aequationes Mathematicae 1992,43(1):59–71. 10.1007/BF01840475

    MathSciNet  Article  MATH  Google Scholar 

  5. 5.

    Brzdęk J: Some remarks on solutions of the functional equation. Publicationes Mathematicae Debrecen 1993,43(1–2):147–160.

    MathSciNet  MATH  Google Scholar 

  6. 6.

    Brzdęk J: The Gołąb-Schinzel equation and its generalizations. Aequationes Mathematicae 2005,70(1–2):14–24. 10.1007/s00010-005-2781-y

    MathSciNet  Article  MATH  Google Scholar 

  7. 7.

    Chudziak J: Approximate solutions of the Gołąb-Schinzel equation. Journal of Approximation Theory 2005,136(1):21–25. 10.1016/j.jat.2005.04.011

    MathSciNet  Article  MATH  Google Scholar 

  8. 8.

    Chudziak J: On a functional inequality related to the stability problem for the Gołąb-Schinzel equation. Publicationes Mathematicae Debrecen 2005,67(1–2):199–208.

    MathSciNet  MATH  Google Scholar 

  9. 9.

    Chudziak J: Stability of the generalized Gołąb-Schinzel equation. Acta Mathematica Hungarica 2006, 113: 115–126.

    MathSciNet  Article  MATH  Google Scholar 

  10. 10.

    Chudziak J, Tabor J: On the stability of the Gołąb-Schinzel functional equation. Journal of Mathematical Analysis and Applications 2005,302(1):196–200. 10.1016/j.jmaa.2004.07.053

    MathSciNet  Article  MATH  Google Scholar 

  11. 11.

    Forti GL: Hyers-Ulam stability of functional equations in several variables. Aequationes Mathematicae 1995,50(1–2):143–190. 10.1007/BF01831117

    MathSciNet  Article  MATH  Google Scholar 

  12. 12.

    Ger R: A collection of problems in stability theory. Report of Meeting, the 38th International Symposium on Functional Equations, June 2000, Noszvaj Aequationes Mathematicae 61 (2001), no. 3, 281–320 Aequationes Mathematicae 61 (2001), no. 3, 281–320

  13. 13.

    Gudder S, Strawther D: Orthogonally additive and orthogonally increasing functions on vector spaces. Pacific Journal of Mathematics 1975,58(2):427–436.

    MathSciNet  Article  MATH  Google Scholar 

  14. 14.

    Hyers DH, Isac G, Rassias ThM: Stability of Functional Equations in Several Variables, Progress in Nonlinear Differential Equations and Their Applications. Volume 34. Birkhäuser Boston, Massachusetts; 1998:vi+313.

    Google Scholar 

Download references

Author information

Affiliations

Authors

Corresponding author

Correspondence to Jacek Chudziak.

Rights and permissions

Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Reprints and Permissions

About this article

Cite this article

Chudziak, J. Approximate solutions of the generalized Gołąb-Schinzel equation. J Inequal Appl 2006, 89402 (2006). https://doi.org/10.1155/JIA/2006/89402

Download citation

Keywords

  • Approximate Solution
\