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International Journal of Mathematics and Mathematical Sciences
Volume 2007 (2007), Article ID 13437, 6 pages
http://dx.doi.org/10.1155/2007/13437
Research Article

Hyers-Ulam-Rassias and Ulam-Gavruta-Rassias Stabilities of an Additive Functional Equation in Several Variables

Department of Mathematics, Faculty of Science, Chulalongkorn University, Bangkok 10330, Thailand

Received 1 June 2007; Revised 12 June 2007; Accepted 24 June 2007

Academic Editor: Martin J. Bohner

Copyright © 2007 Paisan Nakmahachalasint. 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.

Linked References

  1. S. M. Ulam, Problems in Modern Mathematics, chapter~6, John Wiley & Sons, New York, NY, USA, 1964. View at Zentralblatt MATH · View at MathSciNet
  2. D. H. Hyers, “On the stability of the linear functional equation,” Proceedings of the National Academy of Sciences of the United State of America, vol. 27, no. 4, pp. 222–224, 1941. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  3. Th. M. Rassias, “On the stability of the linear mapping in Banach spaces,” Proceedings of the American Mathematical Society, vol. 72, no. 2, pp. 297–300, 1978.
  4. J. M. Rassias, “On approximation of approximately linear mappings by linear mappings,” Journal of Functional Analysis, vol. 46, no. 1, pp. 126–130, 1982. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. J. M. Rassias, “On approximation of approximately linear mappings by linear mappings,” Bulletin des Sciences Mathématiques, vol. 108, no. 4, pp. 445–446, 1984. View at Zentralblatt MATH · View at MathSciNet
  6. J. M. Rassias, “Solution of a problem of Ulam,” Journal of Approximation Theory, vol. 57, no. 3, pp. 268–273, 1989. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. J. M. Rassias, “Solution of a stability problem of Ulam,” Discussiones Mathematicae, vol. 12, pp. 95–103, 1992. View at Zentralblatt MATH · View at MathSciNet
  8. P. Găvruta, “An answer to a question of John M. Rassias concerning the stability of Cauchy equation,” in Advances in Equations and Inequalities, Hadronic Math. Ser., pp. 67–71, Hadronic Press, Palm Harbor, Fla, USA, 1999.
  9. B. Bouikhalene and E. Elqorachi, “Ulam-Gavruta-Rassias stability of the Pexider functional equation,” International Journal of Applied Mathematics & Statistics, vol. 7, no. Fe07, pp. 27–39, 2007.
  10. K. Ravi and M. Arunkumar, “On the Ulam-Gavruta-Rassias stability of the orthogonally Euler-Lagrange type functional equation,” International Journal of Applied Mathematics & Statistics, vol. 7, no. Fe07, pp. 143–156, 2007.
  11. P. Nakmahachalasint, “On the generalized Ulam-Gavruta-Rassias stability of mixed-type linear and Euler-Lagrange-Rassias functional equations,” International Journal of Mathematics and Mathematical Sciences, vol. 2007, Article ID 63239, 10 pages, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. S.-M. Jung, “Hyers-Ulam-Rassias stability of Jensen's equation and its application,” Proceedings of the American Mathematical Society, vol. 126, no. 11, pp. 3137–3143, 1998. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  13. K.-W. Jun and H.-M. Kim, “Stability problem of Ulam for generalized forms of Cauchy functional equation,” Journal of Mathematical Analysis and Applications, vol. 312, no. 2, pp. 535–547, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  14. W.-G. Park and J.-H. Bae, “On a Cauchy-Jensen functional equation and its stability,” Journal of Mathematical Analysis and Applications, vol. 323, no. 1, pp. 634–643, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet