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  • Research Article
  • Open Access

Approximate solutions of the generalized Gołąb-Schinzel equation

Journal of Inequalities and Applications20062006:89402

  • Received: 24 March 2006
  • Accepted: 28 July 2006
  • Published:


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.


  • Approximate Solution


Authors’ Affiliations

Department of Mathematics, University of Rzeszów, Aleja Rejtana 16 C, Rzeszów, 35-959, Poland


  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.View ArticleMATHGoogle Scholar
  2. Brillouët-Belluot N: On some functional equations of Gołąb-Schinzel type. Aequationes Mathematicae 1991,42(2–3):239–270.MathSciNetView ArticleMATHGoogle Scholar
  3. Brillouët-Belluot N, Dhombres J: Équations fonctionnelles et recherche de sous-groupes. Aequationes Mathematicae 1986,31(2–3):253–293.MathSciNetView ArticleMATHGoogle Scholar
  4. Brzdęk J: Subgroups of the group and a generalization of the Gołąb-Schinzel functional equation. Aequationes Mathematicae 1992,43(1):59–71. 10.1007/BF01840475MathSciNetView ArticleMATHGoogle Scholar
  5. Brzdęk J: Some remarks on solutions of the functional equation . Publicationes Mathematicae Debrecen 1993,43(1–2):147–160.MathSciNetMATHGoogle Scholar
  6. Brzdęk J: The Gołąb-Schinzel equation and its generalizations. Aequationes Mathematicae 2005,70(1–2):14–24. 10.1007/s00010-005-2781-yMathSciNetView ArticleMATHGoogle Scholar
  7. Chudziak J: Approximate solutions of the Gołąb-Schinzel equation. Journal of Approximation Theory 2005,136(1):21–25. 10.1016/j.jat.2005.04.011MathSciNetView ArticleMATHGoogle 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.MathSciNetMATHGoogle Scholar
  9. Chudziak J: Stability of the generalized Gołąb-Schinzel equation. Acta Mathematica Hungarica 2006, 113: 115–126.MathSciNetView ArticleMATHGoogle 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.2004.07.053MathSciNetView ArticleMATHGoogle Scholar
  11. Forti GL: Hyers-Ulam stability of functional equations in several variables. Aequationes Mathematicae 1995,50(1–2):143–190. 10.1007/BF01831117MathSciNetView ArticleMATHGoogle 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, 281–320Google Scholar
  13. Gudder S, Strawther D: Orthogonally additive and orthogonally increasing functions on vector spaces. Pacific Journal of Mathematics 1975,58(2):427–436.MathSciNetView ArticleMATHGoogle 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.MATHGoogle Scholar


© Jacek Chudziak. 2006

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.