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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.

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References

  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.

    Book  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  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

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  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

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  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

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  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.

    MATH  Google Scholar 

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Correspondence to Jacek Chudziak.

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

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