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Abstract and Applied Analysis
Volume 2012 (2012), Article ID 435310, 15 pages
http://dx.doi.org/10.1155/2012/435310
Research Article

On a Stability of Logarithmic-Type Functional Equation in Schwartz Distributions

Department of Mathematics, Kunsan National University, Kunsan 573-701, Republic of Korea

Received 29 August 2012; Accepted 18 October 2012

Academic Editor: Abdelghani Bellouquid

Copyright © 2012 Jae-Young Chung. 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, A Collection of Mathematical Problems, Interscience Tracts in Pure and Applied Mathematics, no. 8, Interscience Publishers, New York, NY, USA, 1960.
  2. D. H. Hyers, “On the stability of the linear functional equation,” Proceedings of the National Academy of Sciences of the United States of America, vol. 27, pp. 222–224, 1941. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  3. G. L. Forti, “The stability of homomorphisms and amenability, with applications to functional equations,” Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg, vol. 57, pp. 215–226, 1987. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  4. Z. Daróczy, “On a functional equation of Hosszù type,” Mathematica Pannonica, vol. 10, no. 1, pp. 77–82, 1999. View at Zentralblatt MATH
  5. K. J. Heuvers, “Another logarithmic functional equation,” Aequationes Mathematicae, vol. 58, no. 3, pp. 260–264, 1999. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  6. K. J. Heuvers and P. Kannappan, “A third logarithmic functional equation and Pexider generalizations,” Aequationes Mathematicae, vol. 70, no. 1-2, pp. 117–121, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  7. L. Schwartz, Théorie des Distributions, Hermann, Paris, France, 1966.
  8. J. A. Baker, “Distributional methods for functional equations,” Aequationes Mathematicae, vol. 62, no. 1-2, pp. 136–142, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  9. E. Y. Deeba and E. L. Koh, “The Pexider functional equations in distributions,” Canadian Journal of Mathematics, vol. 42, no. 2, pp. 304–314, 1990. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  10. E. Deeba and S. Xie, “Distributional analog of a functional equation,” Applied Mathematics Letters, vol. 16, no. 5, pp. 669–673, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  11. E. Deeba, P. K. Sahoo, and S. Xie, “On a class of functional equations in distribution,” Journal of Mathematical Analysis and Applications, vol. 223, no. 1, pp. 334–346, 1998. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  12. J. Chung, S.-Y. Chung, and D. Kim, “The stability of Cauchy equations in the space of Schwartz distributions,” Journal of Mathematical Analysis and Applications, vol. 295, no. 1, pp. 107–114, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  13. J. Chung, “Hyers-Ulam stability theorems for Pexider equations in the space of Schwartz distributions,” Archiv der Mathematik, vol. 84, no. 6, pp. 527–537, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  14. J. Chung, “A distributional version of functional equations and their stabilities,” Nonlinear Analysis: Theory, Methods & Applications, vol. 62, no. 6, pp. 1037–1051, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  15. L. Hörmander, The Analysis of Linear Partial Differential Operator I, Springer, Berlin, Germany, 1983.