About this Journal Submit a Manuscript Table of Contents
Abstract and Applied Analysis
Volume 2013 (2013), Article ID 192845, 8 pages
http://dx.doi.org/10.1155/2013/192845
Research Article

On the Intuitionistic Fuzzy Stability of Ring Homomorphism and Ring Derivation

1Department of Mathematics, Hallym University, Chuncheon 200-702, Republic of Korea
2Department of Mathematics, Chungnam National University, 79 Daehangno, Yuseong-gu, Daejeon 305-764, Republic of Korea

Received 7 June 2013; Accepted 25 July 2013

Academic Editor: Bing Xu

Copyright © 2013 Jaiok Roh and Ick-Soon Chang. 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, New York, NY, USA, 1960. 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 States of America, vol. 27, pp. 222–224, 1941. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  3. T. Aoki, “On the stability of the linear transformation in Banach spaces,” Journal of the Mathematical Society of Japan, vol. 2, pp. 64–66, 1950. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. T. 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. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. R. Badora, “On approximate ring homomorphisms,” Journal of Mathematical Analysis and Applications, vol. 276, no. 2, pp. 589–597, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. D. G. Bourgin, “Approximately isometric and multiplicative transformations on continuous function rings,” Duke Mathematical Journal, vol. 16, pp. 385–397, 1949. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. R. Badora, “On approximate derivations,” Mathematical Inequalities & Applications, vol. 9, no. 1, pp. 167–173, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. A. K. Mirmostafaee and M. S. Moslehian, “Fuzzy almost quadratic functions,” Results in Mathematics, vol. 52, no. 1-2, pp. 161–177, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. A. K. Mirmostafaee and M. S. Moslehian, “Fuzzy versions of Hyers-Ulam-Rassias theorem,” Fuzzy Sets and Systems, vol. 159, no. 6, pp. 720–729, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. S. A. Mohiuddine, “Stability of Jensen functional equation in intuitionistic fuzzy normed space,” Chaos, Solitons & Fractals, vol. 42, no. 5, pp. 2989–2996, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. S. A. Mohiuddine, M. Cancan, and H. Şevli, “Intuitionistic fuzzy stability of a Jensen functional equation via fixed point technique,” Mathematical and Computer Modelling, vol. 54, no. 9-10, pp. 2403–2409, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. S. A. Mohiuddine and H. Ševli, “Stability of Pexiderized quadratic functional equation in intuitionistic fuzzy normed space,” Journal of Computational and Applied Mathematics, vol. 235, no. 8, pp. 2137–2146, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  13. M. Mursaleen and S. A. Mohiuddine, “On stability of a cubic functional equation in intuitionistic fuzzy normed spaces,” Chaos, Solitons & Fractals, vol. 42, no. 5, pp. 2997–3005, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  14. R. Saadati and J. H. Park, “On the intuitionistic fuzzy topological spaces,” Chaos, Solitons & Fractals, vol. 27, no. 2, pp. 331–344, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  15. B. Dinda, T. K. Samanta, and U. K. Bera, “Intuitionistic fuzzy Banach algebra,” Bulletin of Mathematical Analysis and Applications, vol. 3, no. 3, pp. 273–281, 2011.